Simple and Pseudo Quadratic Leibniz Superalgebras  

作　　者：Mamadou Pouye Bernardin Kpamegan Leonard Todjihoundé Mamadou Pouye;Bernardin Kpamegan;Leonard Todjihoundé(Institut de Mathématiques et de Sciences Physiques (IMSP), Porto Novo, Bénin;Departement de Mathematiques et Informatique, Université Cheikh Anta Diop, Dakar, Sénégal;Département de Mathématiques, Université Abomey Calavi, Cotonou, Bénin)

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

出　　处：《Journal of Applied Mathematics and Physics》2023年第9期2691-2703,共13页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Leibniz Superalgebras Lie Superalgebras Double Extension Left (Resp. Right) Super-Invariant Bilinear Form 

分 类 号：O15[理学—数学]