Article citationsMore>>

Benayadi, S. and Bouarroudj, S. (2018) Double Extensions of Lie Superalgebras in Characteristic 2 with Nondegenerate Invariant Supersymmetric Bilinear Form. Journal of Algebra, 510, 141-179.
https://doi.org/10.1016/j.jalgebra.2018.06.005

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.