Journal of Lie Theory 32 (2022), No. 4, 917--936
Copyright Heldermann Verlag 2022
On Lie Superalgebras with a Filiform Module as an Odd Part
Elisabete Barreiro
University of Coimbra, CMUC, Department of Mathematics, Coimbra, Portugal
mefb@mat.uc.pt
Said Benayadi
Lab. de Mathématiques, IECL UMR CNRS 7502, Université de Lorraine, Metz, France
said.benayadi@univ-lorraine.fr
Rosa M. Navarro
Departamento de Matemáticas, Universidad de Extremadura, Cáceres, Spain
rnavarro@unex.es
José M. Sánchez
Departamento de Matemáticas, Universidad de Cádiz, Puerto Real, Spain
txema.sanchez@uca.es
[Abstract-pdf]
The aim of this work is on one hand to characterise in any even dimension, via double extensions, a very special family of quadratic Lie superalgebras ${\mathfrak g}={\mathfrak g}_{\bar 0}\oplus {\mathfrak g}_{\bar 1}$ such that ${\mathfrak g}_{\bar 1}$ is a filiform ${\mathfrak g}_{\bar 0}$-module (filiform type). On the other hand, we show that the study of quadratic Lie superalgebras of filiform type can be reduced to those that are solvable. Moreover, we obtain an inductive description of solvable quadratic Lie superalgebras of filiform type via both double extensions and odd double extensions of quadratic ones.
Keywords: Lie superalgebras, quadratic Lie superalgebras, double extensions, solvable, filiform.
MSC: 17A70, 17B05, 17B30.
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