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   Articles with "leibniz" as a keyword



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

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recommendations! 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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recommendations! 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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recommendations! 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

Upper bounds on the dimension of the Schur Lie-multiplier of Lie-nilpotent Leibniz n-algebras

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recommendations! Published in 2024 at "Communications in Algebra"

DOI: 10.1080/00927872.2025.2455456

Abstract: Abstract The Schur Lie -multiplier of Leibniz algebras is the Schur multiplier of Leibniz algebras defined relative to the Liezation functor. In this paper, we study upper bounds for the dimension of the Schur Lie… read more here.

Keywords: lie multiplier; leibniz algebras; algebra; schur lie ... See more keywords

Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators

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recommendations! Published in 2024 at "Forum Mathematicum"

DOI: 10.1515/forum-2023-0268

Abstract: Abstract We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang–Baxter equation (CLYBE) whose skew-symmetric parts are invariant. In addition to triangular Leibniz bialgebras, quasi-triangular Leibniz… read more here.

Keywords: rota baxter; factorizable leibniz; leibniz; leibniz bialgebras ... See more keywords

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

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recommendations! 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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recommendations! 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