Complete sets of representations of classical Lie superalgebras
type: Item
instance of: scholarly article
title: Complete sets of representations of classical Lie superalgebras
zbMATH Open document ID: 0804.17001
DOI: 10.1007/BF00761716
author: Edward S. Letzter
author: Ian M. Musson
published in: Letters in Mathematical Physics
publication date: 1995-01-22T00:00:00Z
review text: A collection of modules over a finite-dimensional complex Lie superalgebra is said to be complete if for every element \(u\neq 0\) in the enveloping algebra there exists a module \(V\) in the collection such that \(u\cdot V\neq 0\). Here it is shown that the finite-dimensional irreducible modules over a finite-dimensional complex Lie superalgebra form a complete set if and only if the even part of the Lie superalgebra is reductive and the universal enveloping algebra is semiprime. For classical Lie superalgebras, these sets are characterized in more detail.
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16P40
Mathematics Subject Classification ID: 16S36
zbMATH DE Number: 606909
zbMATH Keywords: irreducible modules
zbMATH Keywords: complex Lie superalgebra
zbMATH Keywords: complete set
zbMATH Keywords: classical Lie superalgebras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 606909