Author(s)

Mamadou Pouye^1,2, Bernardin Kpamegan³, Leonard Todjihoundé¹

¹Institut de Mathématiques et de Sciences Physiques (IMSP), Porto Novo, Bénin.
²Departement de Mathematiques et Informatique, Université Cheikh Anta Diop, Dakar, Sénégal.
³Département de Mathématiques, Université Abomey Calavi, Cotonou, Bénin.

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.

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

Pouye, M. , Kpamegan, B. and Todjihoundé, L. (2023) Simple and Pseudo Quadratic Leibniz Superalgebras. Journal of Applied Mathematics and Physics, 11, 2691-2703. doi: 10.4236/jamp.2023.119176.