Quadratic (resp. symmetric) Leibniz superalgebras

Benayadi, Saı̈d; Mhamdi, Fahmi; Omri, Salem

doi:10.1080/00927872.2020.1850751

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…For instance, in [7] the authors generalize the notion of double extension and describe quadratic Lie superalgebras; quadratic Leibniz algebras are also studied in [1] and in [8]. The authors in [9] investigate odd quadratic Leibniz superalgebras, in particular they proved that all quadratic Leibniz superalgebras are symmetric and they gave an inductive description of quadratic Leibniz superalgebra. In all these study of quadratic structure, we noticed that the invariance property or the associativity of the bilinear form B (that is…”

Section: Introductionmentioning

confidence: 99%

Simple and Pseudo Quadratic Leibniz Superalgebras

Pouye,

Kpamegan,

Todjihoundé

2023

JAMP

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Compactness of subspaces of a 2  -graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.

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Section: Introductionmentioning

confidence: 99%

Simple and Pseudo Quadratic Leibniz Superalgebras

Pouye,

Kpamegan,

Todjihoundé

2023

JAMP

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“…The present paper is about symmetric (left and right) Zinbiel (super)algebras. This variety of algebras is dual to symmetric Leibniz algebras (about symmetric Leibniz algebras see in [5] and references therein) and it is very thin. As we have proven each symmetric Zinbiel algebra is a 2-step nilpotent or 3-step nilpotent algebra.…”

Section: Introductionmentioning

confidence: 99%

Symmetric Zinbiel superalgebras

Benayadi,

Kaygorodov,

Mhamdi

2022

Preprint

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The notion of symmetric Zinbiel superalgebras is introduced. We prove that the nilpotency index of a symmetric Zinbiel superalgebra is not greater than 4 and describe two-generated symmetric Zinbiel algebras and odd generated superalgebras. We discuss identities of mono and binary symmetric Zinbiel and Leibniz algebras. It is proven that each quadratic Zinbiel algebra is 2-step nilpotent. Also, we study double extensions of symmetric Zinbiel algebras.

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The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras

Álvarez

Kaygorodov

2021

Journal of Algebra

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Quadratic (resp. symmetric) Leibniz superalgebras

Cited by 4 publications

References 22 publications

Simple and Pseudo Quadratic Leibniz Superalgebras

Simple and Pseudo Quadratic Leibniz Superalgebras

Symmetric Zinbiel superalgebras

The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras

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