Odd-quadratic Lie superalgebras with a weak filiform module as an odd part

• Autor(a) principal: Barreiro, Elisabete
• Data de Publicação: 2022
• Outros Autores: Benayadi, Saïd, Navarro, Rosa M., Sánchez, José M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/100188; https://doi.org/10.1016/j.laa.2022.04.013
• topic: Lie superalgebras; Odd-invariant scalar product; Double extensions; Weak filiform; Nilpotent

The aim of this work is to study a very special family of odd-quadratic Lie superalgebras such that is a weak filiform -module (weak filiform type). We introduce this concept after having proved that the unique non-zero odd-quadratic Lie superalgebra with a filiform -module is the abelian 2-dimensional Lie superalgebra such that . Let us note that in this context the role of the center of is crucial. Thus, we obtain an inductive description of odd-quadratic Lie superalgebras of weak filiform type via generalized odd double extensions. Moreover, we obtain the classification, up to isomorphism, for the smallest possible dimensions, that is, six and eight.