Serre-type relations for special linear Lie superalgebras
type: Item
instance of: scholarly article
title: Serre-type relations for special linear Lie superalgebras
zbMATH Open document ID: 0754.17004
DOI: 10.1007/BF00402892
published in: Letters in Mathematical Physics
publication date: 1993-01-16T00:00:00Z
review text: A (complex) simple Lie algebra of rank \(r\) can be defined in terms of \(3r\) (Chevalley) generators and a number of relations (the Serre relations) in which the elements of the Cartan matrix \(A\) appear. Here, the analogous relations are considered for the case where \(A\) is the simplest Cartan matrix of the Lie superalgebra \(sl(m/n)\). Surprisingly, for \(m,n\geq 2\), the Lie superalgebra defined by these generators and relations is not \(sl(m/n)\) but a larger algebra, \(s(m/n)\). It is shown that \(sl(m/n)\) is a nontrivial quotient algebra of \(s(m/n)\), and the supplementary relations are presented. Following this, the relations previously used to define the \(q\)-deformed enveloping algebra \(U_ q(sl(m/n))\) should be modified accordingly.
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 89328
zbMATH Keywords: special linear superalgebra
zbMATH Keywords: quantum enveloping superalgebra
zbMATH Keywords: generators
zbMATH Keywords: Serre relations
zbMATH Keywords: Lie superalgebra
author: M. Scheunert
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 89328