Alfonso Di Bartolo’s research while affiliated with University of Palermo and other places

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Publications (3)


Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra
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June 2024

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80 Reads

Alfonso Di Bartolo

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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 result found in [11], which is only valid when F=C . Moreover, we find the Lie algebra of derivations, its Lie group of automorphisms and the Leibniz algebra of biderivations of L_n. Eventually, we solve the coquecigrue problem for L_n by integrating it into a Lie rack.

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Non-Nilpotent Leibniz Algebras with One-Dimensional Derived Subalgebra

June 2024

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20 Reads

Mediterranean Journal of Mathematics

In this paper we study non-nilpotent non-Lie Leibniz F\mathbb {F} F -algebras with one-dimensional derived subalgebra, where F\mathbb {F} F is a field with char(F)2{\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 abelian algebra. We denote it by LnL_n L n , where n=dimFLnn=\dim _\mathbb {F}L_n n = dim F L n . This generalizes the result found in Demir et al. (Algebras and Representation Theory 19:405-417, 2016), which is only valid when F=C\mathbb {F}=\mathbb {C} F = C . Moreover, we find the Lie algebra of derivations, its Lie group of automorphisms and the Leibniz algebra of biderivations of LnL_n L n . Eventually, we solve the coquecigrue problem for LnL_n L n by integrating it into a Lie rack.


Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra

August 2023

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48 Reads

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 Ln, where n = dimF Ln. This generalizes the result found in [11], which is only valid when F = C . Moreover, we find the Lie algebra of derivations, its Lie group of automorphisms and the Leibniz algebra of biderivations of Ln. Eventually, we solve the coquecigrue problem for Ln by integrating it into a Lie rack.