Manuel Mancini

University of Palermo | UNIPA · Dipartimento di Matematica e Informatica

In this paper we study non-nilpotent non-Lie Leibniz $$\mathbb {F}$$ F -algebras with one-dimensional derived subalgebra, where $$\mathbb {F}$$ F is a field with $${\text {char}}(\mathbb {F}) \ne 2$$ char ( F ) ≠ 2 . We prove that such an algebra is isomorphic to the direct sum of the two-dimensional non-nilpotent non-Lie Leibniz algebra and an abe...

In this paper we study the isotopism classes of two-step nilpotent algebras. We show that every nilpotent Leibniz algebra 𝔤 with dim[𝔤,𝔤]=1 is isotopic to the Heisenberg Lie algebra or to the Heisenberg algebra 𝔩^J1, where J1 is the n × n Jordan block of eigenvalue 1. We also prove that two such algebras are isotopic if and only if the Lie racks in...

In this paper we study the isotopism classes of two-step nilpotent algebras. We show that every nilpotent Leibniz algebra g with dim[g,g]=1 is isotopic to the Heisenberg Lie algebra or to the Heisenberg algebra l_{2n+1}^{J_1}, where J_1 is the n x n Jordan block of eigenvalue 1. We also prove that two such algebras are isotopic if and only if the L...

We study the categorical-algebraic condition of internal actions being weakly representable in the context of non-associative algebras over a field. It is known that such varieties are action accessible if and only if they are Orzech categories of interest and it is also known that both these conditions are implied by weakly representable actions i...

We study the categorical-algebraic condition that internal actions are weakly representable (WRA) in the context of varieties of (non-associative) algebras over a field. Our first aim is to give a complete characterization of action accessible, operadic quadratic varieties of non-associative algebras which satisfy an identity of degree two and to...

In a recent paper, motivated by the study of central extensions of associative algebras, George Janelidze introduces the notion of weakly action representable category. In this paper, we show that the category of Leibniz algebras is weakly action representable and we characterize the class of acting morphisms. Moreover, we study the representabilit...

In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real case of the indecomposable Heisenberg Leibniz algebras are thoroughly described. Finally we show that every a...

In a recent paper, motivated by the study of central extensions of associative algebras, George Janelidze introduces the notion of weakly action representable category. In this paper, we show that the category of Leibniz algebras is weakly action representable and we characterize the class of acting morphisms. Moreover, we study the representabilit...

In this paper we give a complete classification of the Leibniz algebras of biderivations of right Leibniz algebras of dimension up to three over a field F, with characteristic different than two. We describe the main properties of such class of Leibniz algebras and we also compute the biderivations of the four-dimensional Dieudonné Leibniz algebra...

In this paper we study non-nilpotent non-Lie Leibniz F-algebras with one-dimensional derived subalgebra, where F is a field with char(F)≠2. We prove that such an algebra is isomorphic to the direct sum of the two-dimensional non-nilpotent non-Lie Leibniz algebra and an abelian algebra. We denote it by L_n, where n=dimL_n. This generalizes the resul...

In this paper we give a complete classification of the Leibniz algebras of biderivations of right Leibniz algebras of dimension up to three over a field F, with characteristic different than 2. We describe the main properties of such class of Leibniz algebras and we also compute the biderivations of the four-dimensional Dieudonné Leibniz algebra d_...

In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real case of the indecomposable Heisenberg Leibniz algebras are thoroughly described. Finally we show that every a...

In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms. Among these, we describe the complex and the real case of the indecomposable Heisenberg Leibniz algebras as a generalization of the classical (2n+1)-dimensional Heisenberg Lie algebra h2n+1. T...

In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms of Kronecker modules associated with pairs of bilinear forms. Among these, we describe the complex and the real case of the indecomposable Heisenberg Leibniz algebras as a generalization of the classical (2n+1)-dimensional Heisenberg Lie algebra h_{2n+1}...

Il seguente lavoro ha come scopo primario quello di fornire l’analisi e gli esiti di una sperimentazione condotta all’interno delle classi terza e quinta di un liceo scientifico, riguardante rispettivamente l’introduzione della "Crittografia" e della "Teoria della Probabilità". L’articolo è così suddiviso: analisi del contesto culturale e sociale;...