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Universal Central Extensions of Leibniz Superalgebras Over Superdialgebras

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0 Published in 2017 at "Mediterranean Journal of Mathematics"

DOI: 10.1007/s00009-017-0842-9

Abstract: We complete the problem of finding the universal central extension in the category of Leibniz superalgebras of $$\mathfrak {sl}(m, n, D)$$sl(m,n,D) when $$m+n \ge 3$$m+n≥3 and D is a superdialgebra, solving, in particular, the problem… read more here.

Keywords: leibniz superalgebras; superalgebras superdialgebras; central extensions; universal central ... 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

On Leibniz superalgebras which even part is ????????2

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1 Published in 2020 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498821501619

Abstract: This paper deals with Leibniz superalgebras L = L0 ⊕ L1, whose even part is a simple Lie algebra ????????2. We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on... read more here.

Keywords: leibniz superalgebras; part; superalgebras even; even part ... See more keywords

Invariant bilinear forms on Leibniz superalgebras

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0 Published in 2021 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498822500980

Abstract: In [S. Benayadi, F. Mhamdi and S. Omri, Quadratic (resp. symmetric) Leibniz superalgebras, Commun. Algebra, https://doi.org/10.1080/00927872.2020.1850751 ], the quadratic Leibniz superalgebras, which are (left or right) Leibniz superalgebras provided with even supersymmetric non-degenerate and associative… read more here.

Keywords: leibniz superalgebras; benayadi mhamdi; bilinear forms; invariant bilinear ... See more keywords

Solvable Lie and Leibniz superalgebras with a given nilradical

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1 Published in 2020 at "Forum Mathematicum"

DOI: 10.1515/forum-2020-0031

Abstract: Abstract Throughout this paper we show that under certain conditions the method for describing solvable Leibniz (resp. Lie) algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to… read more here.

Keywords: leibniz superalgebras; lie; solvable lie; given nilradical ... See more keywords