Deformations of filiform Lie algebras and superalgebras
type: Item
instance of: scholarly article
title: Deformations of filiform Lie algebras and superalgebras
zbMATH Open document ID: 1257.17031
published in: Journal of Geometry and Physics
publication date: 2010-07-13T00:00:00Z
review text: Expanding previous work on the subject, this paper deals with deformations of the so-called model filiform Lie superalgebra \(L^{n,m}\) that extends naturally the filiform Lie algebra \(L_{n}\). The specific objective of the paper is the analysis and classification of deformations based on cocycles of the space \(Z^{2}(L^{n,m},Z^{2}(L^{n,m})\cap \Hom(L_{n}\wedge L_{n},L_{n})\). This enables to characterize the cocycles of \(L_{n}\) that are also cocycles at the superalgebra level. An algorithm that allows explicit determination of the corresponding bases of cocycles up to \(n\leq 10\) is given.
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 17-08
zbMATH DE Number: 5736303
zbMATH Keywords: Lie algebras
zbMATH Keywords: Lie superalgebras
zbMATH Keywords: cohomology
zbMATH Keywords: deformation
zbMATH Keywords: nilpotent
zbMATH Keywords: filiform
author: Yu. Khakimdjanov
author: R. M. Navarro
reviewed by: Rutwig Campoamor Stursberg
MaRDI profile type: Publication
full work available at URL: j.geomphys.2010.04.007
OpenAlex ID: W1987129042
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DOI: 10.1016/J.GEOMPHYS.2010.04.007
description: scientific article; zbMATH DE number 5736303