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Local and 2-Local Derivations and Automorphisms on Simple Leibniz Algebras

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1 Published in 2019 at "Bulletin of the Malaysian Mathematical Sciences Society"

DOI: 10.1007/s40840-019-00799-5

Abstract: This paper is devoted to study local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We show that all local derivations and 2-local derivations on a finite-dimensional complex simple Leibniz algebra are… read more here.

Keywords: leibniz; automorphisms simple; local derivations; local local ... See more keywords

Some notes on the second homology of Leibniz algebras

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1 Published in 2018 at "Communications in Algebra"

DOI: 10.1080/00927872.2017.1335742

Abstract: ABSTRACT Some properties of the second homology and cover of Leibniz algebras are established. By constructing a stem cover, the second Leibniz homology and cover of abelian, Heisenberg Lie algebras and cyclic Leibniz algebras are… read more here.

Keywords: second homology; notes second; homology leibniz; leibniz algebras ... See more keywords

Quadratic (resp. symmetric) Leibniz superalgebras

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0 Published in 2020 at "Communications in Algebra"

DOI: 10.1080/00927872.2020.1850751

Abstract: Abstract The aim of this article is to study quadratic Leibniz superalgebras, which are (left or right) Leibniz superalgebras with an even supersymmetric non-degenerate and associative bilinear forms. In particular, we prove that this class… read more here.

Keywords: leibniz superalgebras; resp symmetric; symmetric leibniz; quadratic resp ... See more keywords

Generalized metricn-Leibniz algebras and generalized orthogonal representationof metric Lie algebras

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0 Published in 2018 at "TURKISH JOURNAL OF MATHEMATICS"

DOI: 10.3906/mat-1803-61

Abstract: We introduce the notion of a generalized metric n-Leibniz algebra and show that there is a one-to-one correspondence between generalized metric n-Leibniz algebras and faithful generalized orthogonal representations of metric Lie algebras (called Lie triple… read more here.

Keywords: lie algebras; metric lie; leibniz algebras; generalized orthogonal ... See more keywords

Split regular Hom-Leibniz color 3-algebras

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0 Published in 2019 at "Colloquium Mathematicum"

DOI: 10.4064/cm7671-9-2018

Abstract: We introduce and describe the class of split regular $Hom$-Leibniz color $3$-algebras as the natural extension of the class of split Lie algebras, split Leibniz algebras, split Lie $3$-algebras, split Lie triple systems, split Leibniz… read more here.

Keywords: split regular; hom leibniz; regular hom; split ... See more keywords