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Title: Odd-quadratic Lie superalgebras with a weak filiform module as an odd part
Authors: Barreiro, Elisabete 
Benayadi, Saïd 
Navarro, Rosa M.
Sánchez, José M. 
Keywords: Lie superalgebras; Odd-invariant scalar product; Double extensions; Weak filiform; Nilpotent
Issue Date: 2022
Publisher: Elsevier
Project: info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB/00324/2020/PT/Center for Mathematics, University of Coimbra 
Serial title, monograph or event: Linear Algebra and Its Applications
Volume: 649
Abstract: 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.
ISSN: 00243795
DOI: 10.1016/j.laa.2022.04.013
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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