A complete description of all the infinitesimal deformations of the Lie superalgebra \(L^{n,m}\)
type: Item
instance of: scholarly article
title: A complete description of all the infinitesimal deformations of the Lie superalgebra \(L^{n,m}\)
zbMATH Open document ID: 1254.17019
published in: Journal of Geometry and Physics
publication date: 2010-01-08T00:00:00Z
review text: The aim of this work is to complete the description and classification of infinitesimal deformations of the model Lie superalgebra \(L^{n,m}\) given by the brackets \([X_{0},X_{i}] = X_{i+1}\) (\(1\leq i \leq n-1\)) and \([X_{0},Y_{j}] = Y_{j+1}\) (\(1\leq j \leq m-1\)) over a basis \(X_{0},X_{1},\dots ,X_{n},Y_{1},\dots ,Y_{m}\). In analogy with the case of Lie algebras, it turns out that this superalgebra is the main structure from which all filiform superalgebras can be derived by means of infinitesimal deformations. The authors give an explicit decomposition of the cohomology space \(Z^{2}(L^{n,m},Z^{2}(L^{n,m})\) and bases of all its components.
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 5655064
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.2009.09.002
OpenAlex ID: W2040798466
cites work: Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes
cites work: Some deformations of nilpotent Lie superalgebras
cites work: Infinitesimal deformations of the Lie superalgebra \(L^{n,m}\)
cites work: Deformations of filiform Lie algebras and superalgebras
cites work: Q4261815
cites work: Q3819212
cites work: The theory of Lie superalgebras. An introduction
cites work: Cohomology of Lie superalgebras and their generalizations
cites work: Some problems concerning to nilpotent Lie superalgebras
cites work: Q4095018
cites work: Q3892399
DOI: 10.1016/J.GEOMPHYS.2009.09.002
description: scientific article; zbMATH DE number 5655064