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Vishnyakova, E. (2016) Double Extension for Commutative n-ary Superalgebras with a Skew-Symmetric Invariant Form. Banach Center Publications, 110.
https://doi.org/10.4064/bc110-0-18

has been cited by the following article:

• TITLE: Simple and Pseudo Quadratic Leibniz Superalgebras

  AUTHORS: Mamadou Pouye, Bernardin Kpamegan, Leonard Todjihoundé

  KEYWORDS: Leibniz Superalgebras, Lie Superalgebras, Double Extension, Left (Resp. Right) Super-Invariant Bilinear Form

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.9, September 28, 2023

  ABSTRACT: Compactness of subspaces of a Z2-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.