Sergei Silvestrov

Mälardalen University | MDH · Division of Applied Mathematics. School of Education, Culture and Communication

The purpose of this paper is to introduce the class of noncommutative $3$-BiHom-Poisson color algebras, which is a combination of $3$-BiHom-Lie color algebras and BiHom-associative color algebras under a compatibility condition, called BiHom-Leibniz color identity, and then study their representations and associated Kupershmidt operators. In additi...

The aim of this paper is to study the sufficient conditions for the existence of fixed points of Perov type T -contractive mappings in the setup of complete cone b -metric space associated with generalized c -distance. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and gen...

In this paper, we study the generalized F-iterated function system in G-metric space. Several results of common attractors of generalized iterated function systems obtained by using generalized F-Hutchinson operators are also established. We prove that the triplet of F-Hutchinson operators defined for a finite number of general contractive mappings...

The aim of this work is to investigate the properties and classification of an interesting class of 4-dimensional 3-Hom-Lie algebras with a nilpotent twisting map α and eight structure constants as parameters. Derived series and central descending series are studied for all algebras in this class and are used to divide it into five non-isomorphic s...

In this work, we present methods for constructing representations of polynomial covariance type commutation relations $$AB=BF(A)$$ A B = B F ( A ) by linear integral operators in Banach spaces $$L_p$$ L p . We derive necessary and sufficient conditions on the kernel functions for the integral operators to satisfy the covariance type commutation rel...

Elduque-Myung type mutations of general, possibly non-associative, algebras and of several classes of Hom-algebras are explored. Several extensions of the results from scalar and non-scalar mutations of associative algebras to mutations of non-associative algebras and of several kinds of hom-algebras of hom-associative type are obtained, including...

In this paper, we present the generalized iterated function system for the construction of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors’ problems of rational contraction maps in the framework of dislocated metric spaces is also established. Moreover, the generalized c...

This study is concerned with induced ternary Hom-Lie-Nambu Lie algebras from Hom-Lie algebras and their classification. The induced algebras are constructed from a class of Hom-Lie algebra with nilpotent linear map. The families of ternary Hom-Nambu-Lie arising in this way of construction are classified for a given class of nilpotent linear maps. I...

In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition of the generalized derivation depends on some parameters \( (\lambda ,\mu ,\gamma )\in \mathbb {C}^{3}\). In pa...

In this paper, the representations of color hom-Lie algebras have been reviewed and the existence of a series of coboundary operators is demonstrated. Moreover, the notion of a color omni-hom-Lie algebra associated to a linear space and an even invertible linear map have been introduced. In addition, characterization method for regular color hom-Li...

In this paper we examine interactions between \((\sigma ,\tau )\)-derivations via commutator and consider new n-ary structures based on twisted derivation operators. We show that the sums of linear spaces of \((\sigma ^k,\tau ^l)\)-derivations and also of some of their subspaces, consisting of twisted derivations with some commutation relations wit...

The aim of this work is to study properties of n-Hom-Lie algebras in dimension \(n+1\) allowing to explicitly find them and differentiate them, to eventually classify them. Some specific properties of \((n+1)\)-dimensional n-Hom-Lie algebra such as nilpotence, solvability, center, ideals, derived series and central descending series are studied, th...

Constructions of n-ary bialgebras and n-ary infinitesimal bialgebras of associative type and their hom-analogs, generalizing the hom-bialgebras and infinitesimal hom-bialgebras are investigated. Main algebraic characteristics of n-ary totally, n-ary weak totally, n-ary partially and n-ary alternate partially associative algebras and bialgebras, and...

We compare and examine the influence of Hom-associativity, involving a linear map twisting the associativity axiom, on fundamental aspects important in study of Hom-algebras and \((\sigma ,\tau )\)-derivations satisfying a \((\sigma ,\tau )\)-twisted Leibniz product rule in connection to Hom-algebra structures. As divisibility may be not transitive...

The purpose of this paper is to introduce Hom-prealternative superalgebras and their bimodules. Some constructions of Hom-prealternative superalgebras and Hom-alternative superalgebras are given, and their connection with Hom-alternative superalgebras are studied. Bimodules over Hom-prealternative superalgebras are introduced, relations between bim...

Representations of polynomial covariant type commutation relations by pairs of linear integral operators and multiplication operators on Banach spaces \(L_p\) are constructed.

In this paper we discuss the extension of the Wishart probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras. The symmetric cones form a basis for the construction of the degenerate and non-degenerate Wishart distributions in the field of \({{\,\textrm{Herm}\,}}(m,\mathbb {C})\), \({{\,\...

The aim of this work is to study properties of n-Hom-Lie algebras in dimension \(n+1\) allowing to explicitely find them and differentiate them, to eventually classify them. Specifically, the n-Hom-Lie algebras in dimension \(n+1\) for \(n=4,5,6\) and nilpotent \(\alpha \) with 2-dimensional kernel are computed and some detailed properties of these...

Representations of polynomial covariance type commutation relations are constructed on Banach spaces \(L_p\) and \(C[\alpha , \beta ]\ \alpha ,\beta \in \mathbb {R}\). Representations involve operators of multiplication with piecewise functions, multiplication operators and inner superposition operators.

In this paper, we study some equivalent conditions for a color hom-Lie algebra to be a complete color hom-Lie algebra. In particular, we discuss the relationship between decomposition and completness for a color hom-Lie algebra. Moreover, we check some conditions that the set of \(\alpha ^{s}\)-derivations of a color hom-Lie algebra to be complete...

The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimen...

For the space of \((\sigma ,\tau )\)-derivations of the group algebra \( \mathbb {C} [G] \) of a discrete countable group G, the decomposition theorem for the space of \((\sigma ,\tau )\)-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characte...

This paper addresses a Hom-associative algebra built as a direct sum of a given Hom-associative algebra \((\mathcal {A}, \cdot , \alpha )\) and its dual \((\mathcal {A}^{*}, \circ , \alpha ^{*}),\) endowed with a non-degenerate symmetric bilinear form \(\mathcal {B},\) where \(\cdot \) and \(\circ \) are the products defined on \(\mathcal {A}\) and...

The main feature of color Hom-algebras is that the identities defining the structures are twisted by even linear maps. The purpose of this paper is to introduce and give some constructions of admissible Hom-Novikov-Poisson color Hom-algebras and Hom-Gelfand-Dorfman color Hom-algebras. Their bimodules and matched pairs are defined and the relevant p...

In this paper we consider crossed product algebras of piecewise constant function algebras on the real line that arise in multiresolution analysis. Such algebras form an increasing sequence of algebras of functions on the real line. We derive conditions under which these algebras are invariant under a bijection on the real line, in which case we ge...

Basic definitions and properties of nearly associative algebras are described. Nearly associative algebras are proved to be Lie-admissible algebras. Two-dimensional nearly associative algebras are classified, and main classes are derived. The bimodules, matched pairs and Manin triple of a nearly associative algebras are derived and their equivalenc...

In this paper, we expose a geometrical interpretation of the q-Wallis formula. We construct plane regions which consist of rectangles whose edges’ lengths are directly connected with factors in this formula. These regions are bounded by quarters of inside and outside circles from which we get estimates and conclusions about the number \(\pi _q\).

Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and generalize many results in the existing literature.

Generalized (rational) graph contractions in the framework of a dislocated metric space endowed with a directed graph are investigated. Fixed point results for set-contractions are obtained. We also provide some examples to illustrate our main results. Moreover, the well-posedness of obtained fixed point results are also shown. Our obtained results...

The existence and uniqueness of the common fixed point for generalized contractive mappings in order partial metric spaces is investigated. The existence of nonnegative solution of implicit nonlinear integral equations is also studied. Some examples demonstrating the validity of our main results are constructed. The presented results extend and uni...

The aim of this work is to explore some properties of n-ary skew-symmetric Hom-algebras and n-Hom-Lie algebras related to their ideals, derived series and central descending series. We extend the notions of derived series and central descending series to n-ary skew-symmetric Hom-algebras and provide various general conditions for their members to b...

Using the setting of $G$-metric spaces, common fixed point theorems for four maps satisfying the weakly commuting conditions are obtained for various generalized contractive conditions. Several examples are also presented to show the validity of main results.

Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance commutation relations by pairs consisting of a differential and linear integral operator are considered inclu...

Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by integral operators are studied both for general polynomial covariance commutation relations and for important clas...

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations extending simultaneously the covariance and the reciprocal covariance type commutation relations. Necessary and suff...

Representations of polynomial covariant type commutation relations by pairs of linear integral operators and multiplication operators on Banach spaces $L_p$ are constructed.

Representations of polynomial covariance type commutation relations are constructed on Banach spaces $L_p$ and $C[\alpha, \beta],\ \alpha,\beta\in \mathbb{R}$. Representations involve operators with piecewise functions, multiplication operators and inner superposition operators.

Using the setting of ordered metric spaces, we obtain common end point of two multivalued mappings satisfying a generalized $(\psi,\varphi)$-weak contractive condition. Under comparative condition on the set of end points of multivalued mappings, our results assure the uniqueness of the end point. These results generalize and improve several recent...

Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance type commutation relations are obtained in terms of their kernels. For important classes of polynomial covariance...

In this paper, we present the generalized iterated function system for constructing of common fractals of generalized contractive mappings in the setup of dislocated metric spaces. The well-posedness of attractors based problems of rational contraction maps in the framework of dislocated metric spaces is also established. Moreover, the generalized...

The aim of this work is to investigate the properties and classification of an interesting class of $4$-dimensional $3$-Hom-Lie algebras with a nilpotent twisting map $\alpha$ and eight structure constants as parameters. Derived series and central descending series are studied for all algebras in this class and are used to divide it into five non-i...

A notion of a Hom-Leibniz bialgebra is introduced and it is shown that matched pairs of Hom-Leibniz algebras, Manin triples of Hom-Leibniz algebras and Hom-Leibniz bialgebras are equivalent in a certain sense. A notion of Hom-Leibniz dendriform algebra is established, their bimodules and matched pairs are defined and their properties and theorems a...

The aim of this paper is to give some constructions results of averaging operators on Hom-Lie algebras. The homogeneous averaging operators on $q$-deformed Witt and $q$-deformed $W(2,2)$ Hom-algebras are classified. As applications, the induced Hom-Leibniz algebra structures are obtained and their multiplicativity conditions are also given.

The purpose of this paper is to study pseudo-Euclidean and symplectic Hom-alternative superalgebras and discuss some of their proprieties and provide construction procedures. We also introduce the notion of Rota-Baxter operators of pseudo-Euclidean Hom-alternative superalgebras of any weight and Hom-post-alternative superalgebras. A Hom-post-altern...

Complete hom-Lie superalgebras are considered and some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra are established. In particular, the relation between decomposition and completeness for a hom-Lie superalgebra is described. Moreover, some conditions that the linear space of αs\documentclass[12pt]{minimal}...

An analysis is carried out to study the flow and heat transfer of electrically conducting immiscible viscous fluids in a parallel vertical channel. Both fluids are incompressible and the flow is assumed to be steady, one dimensional and fully developed. Combined free and forced convection inside the channel is considered. Through proper choice of d...

Several generalised contractive type conditions are established for existence, uniqueness and well-posedness of the fixed point results, limit shadowing property, and also forNazir, Talat Silvestrov, Sergei the property of coincidence of sets of periodic points and fixed points for cyclic contractive maps on multiplicative metric spaces.

In graph theory, centrality measures are very crucial in ranking vertices of the graph in order of their importance. Alpha and eigenvector centralities are some of the highly placed centrality measures applied especially in social network analysis, disease diffusion networks and mechanical infrastructural developments. In this study we focus on rec...

We investigate the periodic points and common fixed point of generalized contraction mappings self-mappings in the setup of multiplicative metric spaces. We also study the well-posedness for the obtained results. The common fixed point results of mappings involved in the cyclic representation are also obtained. Moreover, some applications to obtain...

We introduce a random version of some known faster fixed point iterative processes and approximate the random fixed point of a generalized random operator using these random iterative processes. Moreover, the Bochner integrability of the random fixed points for this kind of generalized random operators and the almost sure T-stability of these rando...

We study the double-mean-reverting model by Gatheral. Our previous results concerning the asymptotic expansion of the implied volatility of a European call option, are improved up to order 3, that is, the error of the approximation is ultimately smaller that the 1.5th power of time to maturity plus the cube of the absolute value of the difference b...

The fixed point results of T-Hardy Rogers type mappings that are satisfying generalized contractive conditions in the setup of multiplicative metric spaces are investigated. The well-posedness and limit shadowing property of T-Hardy Rogers type mappings are also established. Furthermore, periodic point property of these contraction mappings are als...

Representations of polynomial covariance type commutation relations by linear integral operators on Lp over measures spaces are constructed. Conditions for such representations are described in terms of kernels of the corresponding integral operators. Representation by integral operators are studied both for general polynomial covariance commutatio...

The extreme points of Vandermonde determinants when optimized on surfaces like spheres and cubes have various applications in random matrix theory, electrostatics and financial mathematics. In this study, we apply the extreme points Vandermonde determinant when optimized on various surfaces to risk minimization in financial mathematics. We illustra...

In this paper Muhumuza, Asaph KeikaraLundengård, KarlMalyarenko, AnatoliySilvestrov, SergeiMango, John MageroKakuba, Godwinwe demonstrate the extreme points of the Wishart joint eigenvalue probability distributions in higher dimension based on the boundary points of the symmetric cones in Jordan algebras. The extreme points of the Vandermonde deter...

The purpose of this paper is to study the $\mathcal{O}$-operators on Malcev algebras and discus the solutions of Malcev Yang-Baxter equation by $\mathcal{O}$-operators. Furthermore we introduce the notion of weighted $\mathcal{O}$-operators on Malcev algebras, which can be characterized by graphs of the semi-direct product Malcev algebra . Then we...

The main feature of Hom-algebras is that the identities defining the structures are twisted by linear maps. The purpose of this paper is to introduce and study a Hom-type generalization of pre-Malcev algebras, called Hom-pre-Malcev algebras. We also introduce the notion of Kupershmidt operators of Hom–Malcev and Hom-pre-Malcev algebras and show the...

Fixed point results of Perov type mapping which satisfy generalized Tcontractive conditions in the setup of cone b-metric spaces associated with generalized c-distance are proved and illustrated by nontrivial examples.

The purpose of this paper is to study the $\mathcal{O}$-operators on Malcev algebras and discuss the solutions of Malcev Yang-Baxter equation by $\mathcal{O}$-operators. Furthermore we introduce the notion of weighted $\mathcal{O}$-operators on Malcev algebras, which can be characterized by graphs of the semi-direct product Malcev algebra. Then we...

The main goal of this work is to introduce the notion of Hom-M-dendriform algebras which are the dendriform version of Hom-Malcev algebras. In fact they are the algebraic structures behind the $\mathcal{O}$-operator of Hom-pre-Malcev algebras. They also fit into a bigger framework as Hom-Malcev algebraic analogues of Hom-L-dendriform algebras. Furt...

The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of dihedral quandles over fi...

The main feature of Hom-algebras is that the identities defining the structures are twisted by linear maps. The purpose of this paper is to introduce and study a Hom-type generalization of pre-Malcev algebras, called Hom-pre-Malcev algebras. We also introduce the notion of Kupershmidt operators of Hom-Malcev and Hom-pre-Malcev algebras and show the...

The main feature of color Hom-algebras is that the identities defining the structures are twisted by even linear maps. The purpose of this paper is to introduce and give some constructions of admissible Hom-Novikov-Poisson color Hom-algebras and Hom-Gelfand-Dorfman color Hom-algebras. Their bimodules and matched pairs are defined and the relevant p...

The aim of this paper is to introduce and to develop several methods for constructions of BiHom-X algebras by extending composition methods, and by using Rota-Baxter operators and some elements of centroids. The bimodules of BiHom-left symmetric dialgebras, BiHom-associative dialgebras and BiHom-tridendriform algebra are defined, and it is shown th...

Several recent results concerning Hom-Leibniz algebra are reviewed, the notion of symmetric Hom-Leibniz superalgebra is introduced and some properties are obtained. Classification of 2-dimensional Hom-Leibniz algebras is provided. Centroids and derivations of multiplicative Hom-Leibniz algebras are considered including the detailed study of 2-dimen...

Complete hom-Lie superalgebra are considered and some equivalent conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra are established. In particular, the relation between decomposition and completeness for a hom-Lie super-algebra is described. Moreover, some conditions that the set of α s-derivations of a hom-Lie superalgebra...

The notion of a Hom-Leibniz bialgebra is introduced and it is shown that matched pairs of Hom-Leibniz algebras, Manin triples of Hom-Leibniz algebras and Hom-Leibniz bialgebras are equivalent in a certain sense. The notion of Hom-Leibniz dendriform algebra is established, their bimodules and matched pairs are defined and their properties and theore...

We introduce a concept of 3-Lie-Rinehart superalgebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we study the relationships between a Lie-Rinehart superalgebra and its induced 3-Lie-Rinehart superalgebra. The deformations of 3-Lie-Rinehart superalgebra are considered via a cohomology theory.

Eigenvector centrality is one of the outstanding measures of central tendency in graph theory. In this paper we consider the problem of calculating eigenvector centrality of graph partitioned into components and how this partitioning can be used. Two cases are considered; first where the a single component in the graph has the dominant eigenvalue,...

The aim of this paper is to generalise the construction of n -ary Hom-Lie bracket by means of an $$(n-2)$$ ( n - 2 ) -cochain of given Hom-Lie algebra to super case inducing n -Hom-Lie superalgebras. We study the notion of generalized derivations and Rota-Baxter operators of n -ary Hom-Nambu and n -Hom-Lie superalgebras and their relation with gene...

The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of \emph{dihedral quandles}...

The notions of transposed Hom-Poisson and Hom-pre-Lie Poisson algebras are introduced. Their bimodules and matched pairs are defined and the relevant properties and theorems are given. The notion of Manin triple of transposed Hom-Poisson algebras is introduced, and its equivalence to the transposed Hom-Poisson bialgebras is investigated. The notion...

The aim of this paper is to introduce and to give some constructions results of BiHom-X algebras by using Yau's twisting, Rota Baxter and Some elements of centroids. Next, we define the bimodules of BiHom-left symmetric dialgebras, BiHom-associative dialgebras and BiHom-tridendriform algebras. A sequence of this kind of bimodules can be constructed...

The main feature of Hom-algebras is that the identities defining the structures are twisted by linear maps. The purpose of this paper is to introduce and study a Hom-type generalization of pre-Malcev algebras and M-dendriform algebras, called Hom-pre-Malcev algebras and Hom-M-dendriform algebras. We also introduce the notion of $\mathcal{O}$-operat...

PageRank is a widely used hyperlink‐based algorithm for estimating the relative importance of nodes in networks. In this chapter, the authors formulate the PageRank problem as a first‐ and second‐order Markov chains perturbation problem. Using numerical experiments, they compare convergence rates for different values of perturbation parameter on di...

This chapter examines some properties of the extreme points of the probability density distribution of the Wishart matrix, using properties of the Vandermonde determinant and showing examples of the applications of these properties. It gives a brief outline on the background of the problem setup, based on polynomial regression models and the close...

Gatheral's double‐mean‐reverting model by is motivated by empirical dynamics of the variance of stock price. In this chapter, the authors study the behavior of the implied volatility with respect to the logarithmic strike price and maturity near expiry and at‐the‐money. Using the method by Pagliarani and Pascucci, they explicitly calculate the firs...

A PageRank update refers to the process of computing new PageRank values after a change(s) (addition or removal of links/vertices) has occurred in real‐life networks. In this chapter, the authors focus on updating the scaled adjacency matrix, maintaining levels and calculating the PageRank of a tree graph after some changes. They propose a techniqu...

This chapter is devoted to studies of perturbed Markov chains, commonly used for the description of information networks. It presents the results of detailed perturbation analysis of Markov chains with damping component and numerical experiments supporting and illustrating the results of this perturbation analysis. The chapter describes continuity...

In risk management, foreign investors or multinational corporations are highly interested in knowing how volatile a currency is in order to hedge risk. In this chapter, using daily exchange rates and the exponential weighted moving average (EWMA) model, the authors perform volatility forecasting. They investigate how the use of the available time s...

When working with a network, it is often of interest to locate the “most important” nodes in the network. A common way to do this is by using some graph centrality measures. In this chapter, the authors focus on the centrality measures based on powers of the adjacency matrix and those based on random walk. They introduce the concept of linear syste...

The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly,...

The goal of this paper is to introduce and give some constructions and study properties of Hom-left-symmetric color dialgebras and Hom-tridendriform color algebras. Next, we study their connection with Hom-associative color algebras, Hom-post-Lie color algebras and Hom–Poisson color dialgebras. Finally, we generalize Yau’s twisting to a class of co...

Basic definitions and properties of nearly associative algebras are described. Nearly associative algebras are proved to be Lie-admissible algebras. Two-dimensional nearly associative algebras are classified, and its main classes are derived. The bimodules, matched pairs and Manin triple of a nearly associative algebras are derived and their equiva...

The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincar\'e-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.

In this paper, we generalize the results about generalized derivations of Lie algebras to the case of BiHom-Lie algebras. In particular we give the classification of generalized derivations of Heisenberg BiHom-Lie algebras. The definition of the generalized derivation depends on some parameters $ (\lambda,\mu,\gamma)\in \mathbb{C}^{3}. $ In particu...

The space of possible Hom-Lie structures on complex 4-dimensional Lie algebras is considered in terms of linear maps that turn the Lie algebras into Hom-Lie algebras. Hom-Lie structures on the representatives of isomorphism classes of complex 4-dimensional Lie algebras are described.

Representations of color Hom-Lie algebras are reviewed, and it is shown that there exist a series of coboundary operators. We also introduce the notion of a color omni-Hom-Lie algebra associated to a vector space and an even invertible linear map. We show how regular color Hom-Lie algebra structures on a vector space can be characterized. Moreover,...

In this paper we investigate some important basic properties of simple Hom-Lie superalgebras and show that a Hom-Lie superalgebra does not have any left or right non trivial ideals. Moreover, we classify invariant bilinear forms on a given simple Hom-Lie superalgebra. Then we study the Killing forms on a Hom-Lie algebra which are examples of the in...

We introduce the concept of 3-Lie-Rinehart superalgebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we study the relationships between a Lie-Rinehart superalgebra and its induced 3-Lie-Rinehart superalgebra. The deformations of 3-Lie-Rinehart superalgebra are considered via the cohomology theory...

This paper addresses a Hom-associative algebra built as a direct sum of a given Hom-associative algebra $(\mathcal{A}, \cdot, \alpha)$ and its dual $(\mathcal{A}^{\ast}, \circ, \alpha^{\ast}),$ endowed with a non-degenerate symmetric bilinear form $\mathcal{B},$ where $\cdot$ and $\circ$ are the products defined on $\mathcal{A}$ and $\mathcal{A}^{\...

For the space of $(\sigma,\tau)$-derivations of the group algebra $ \mathbb{C} [G] $ of discrete countable group $G$, the decomposition theorem for the space of $(\sigma,\tau)$-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characters. Several...

We show that, having a Hom-Lie algebra and an element of its dual vector space that satisfies certain conditions, one can construct a ternary totally skew-symmetric bracket and prove that this ternary bracket satisfies the Hom-Filippov-Jacobi identity, i.e. this ternary bracket determines the structure of 3-Hom-Lie algebra on the vector space of a...

In this paper we consider commutants in crossed product algebras, for algebras of piece-wise constant functions on the real line acted on by the group of integers \(\mathbb {Z}\). The algebra of piece-wise constant functions does not separate points of the real line, and interplay of the action with separation properties of the points or subsets of...

The fixed and common fixed point problems of selfmappings that are satisfying certain type generalized integral contractions in the setup of multiplicative metric spaces are investigated. Well-posedness results for fixed point problem of maps under restrictions of integral type contractions are obtained. Moreover, the periodic points results of gen...

We derive conditions for an arbitrary n-dimensional algebra to be a Hom-Lie algebra, in the form of a system of polynomial equations, containing both structure constants of the skew-symmetric bilinear map and constants describing the twisting linear endomorphism. The equations are linear in the constants representing the endomorphism and non-linear...

We consider a market model with four correlated factors and two stochastic volatilities, one of which is rapid-changing, while another one is slow-changing in time. An advanced Monte Carlo method based on the theory of cubature in Wiener space is used to find the no-arbitrage price of the European call option in the above model.