Mohammed Wadia Mansouri

• Ibn Tofaïl University

We introduce the notion of cosymplectic structure on Jacobi-Jordan algebras, and we state that they are related to symplectic Jacobi-Jordan algebras. We show, in particular, that they support a right-skew-symmetric product. We also study the double extension constructions of cosymplectic Jacobi-Jordan algebras and give a complete classification in...

Topological approaches for protein structure analysis often comes with an input matrix describing the suitable filtration of our data and helping to choose adequate statistical tests to come up with a final shape by using an algebraic invariant, which is in our case a persistent diagram, we will be giving a theoretical description of this matrix th...

Persistent homology is a new tool from algebraic topology, showing until nowadays a lot of success when it comes to application in biology since this latest use metrics only for measuring similarities, Embedding the geometric details and focusing on the global shape is the key point making the success of persistent homology as an efficient topologi...

Persistent homology is a tool from a set of methods called Topological data analysis, showing until nowadays a lot of success when it comes to application in biology since this latest uses metrics only for measuring similarities, Embedding the geometric details and focusing on the global shape is the key point making the success of persistent homol...

Persistent homology is a new tool from algebraic topology, showing until nowadays a lot of success when it comes to application in biology since this latest use metrics only for measuring similarities, Embedding the geometric details and focusing on the global shape is the key point making the success of persistent homology as an efficient topologi...

In this paper, we classify eight-dimensional non-solvable Lie algebras that support a symplectic structure. As well as a complete classification is given, up to symplectomorphism, of eight-dimensional symplectic non-solvable Lie algebras.

We give some properties of cosymplectic Lie algebras, we show, in particular, that they support a left symmetric product. We also give some constructions of cosymplectic Lie algebras, as well as a classification in three and five-dimensional cosymplectic Lie algebras.

We give some properties of cosymplectic Lie algebras, we show, in particular, that they support a left symmetric product. We also give some constructions of cosymplectic Lie algebras, as well as a classification in three and five-dimensional cosymplectic Lie algebras.

We give a complete classification of left invariant para-Kähler structures on four-dimensional simply connected Lie groups up to an automorphism. As an application we discuss some curvatures properties of the canonical connection associated to these structures as flat, Ricci flat and existence of Ricci solitons.

It is well known that a symplectic Lie algebra admits a left symmetric product. In this work, we study the case where this product is Novikov, we show that the left-symmetric product associated to the symplectic Lie algebra is Novikov if and only if it is associative. In this case, the symplectic Lie algebra is called symplectic Novikov Lie algebra...

The paper deals with linearization problem of Poisson-Lie structures on the \((1+1)\) Poincaré and \(2D\) Euclidean groups. We construct the explicit form of linearizing coordinates of all these Poisson-Lie structures. For this, we calculate all Poisson-Lie structures on these two groups mentioned above, through the correspondence with Lie Bialgebr...

It is well known that a symplectic Lie algebra admit a left symmetric product. In this work, we study the case where this product is Novikov, we show that the left-symmetric product associated to the symplectic Lie algrbra is Novikov if and only if it is associative. In this case the symplectic Lie algebra is called symplectic Novikov Lie algebra(S...

We give a complete classification of left invariant generalized complex structures of type 1 on four dimensional simply connected Lie groups and we compute for each class its invariant generalized Dolbeault cohomology, its invariant generalized Bott-Chern cohomology and its invariant generalized Aeppli cohomology. We classify also left invariant ge...

We give a complete classification of left invariant para-K\"ahler structures on four-dimensional simply connected Lie groups up to an automorphism. As an application we discuss some curvatures properties of the canonical connection associated to these structures as flat, Ricci flat and existence of Ricci solitons.

We give a complete classification of left invariant generalized complex structures of type 1 on four dimensional simply connected Lie groups and we compute for each class its invariant generalized Dolbeault cohomology, its invariant generalized Bott-Chern cohomology and its invariant generalized Aeppli cohomology. We classify also left invariant ge...

We give a complete classification of left invariant generalized complex structures of type 1 on four dimensional simply connected Lie groups and we compute for each class its invariant generalized Dolbeault cohomology, its invariant generalized Bott-Chern cohomology and its invariant generalized Aeppli cohomology. We classify also left invariant ge...

In this paper, we give a complete classification of Lagrangian and bi-Lagrangian subalgebras, up to an inner automorphism on $\frak{aff}(2,\mathbb{R})$, and compute the curvatures of some bi-Lagrangian structures.

We show that on any Poisson–Lie group, the effect of the dressing vector fields on volume forms generates a class on Poisson cohomology. The comparison with the modular class give rise to a complete Poisson vector field related to the modular group.

We show the conformal invariance of the Poisson-Lie group SU(2) by dressing transformations. This construction gives in particular a Poisson cohomology class of the group SU(2).