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.