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Benayadi, S. and Hidri, S. (2016) Leibniz Algebras with Invariant Bilinear Form and Related Lie Algebra. Communication in Algebra, 44, 3538-3556.
https://doi.org/10.1080/00927872.2015.1085550

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.