``Mass formulae'' for tensor operators connected with Lie superalgebras
type: Item
instance of: scholarly article
title: ``Mass formulae'' for tensor operators connected with Lie superalgebras
zbMATH Open document ID: 0697.17002
DOI: 10.1007/BF00399969
author: Kazimierz Brągiel
published in: Letters in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: Let \({\mathfrak g}\) be a finite-dimensional complex Lie superalgebra and let E and F be finite-dimensional graded \({\mathfrak g}\)-modules. It is well- known that L(F), the space of all linear mappings of F into itself, carries a canonical structure of a graded g-module. A tensor operator of type E and operating in F is a homomorphism of the graded \({\mathfrak g}\)- module E into the graded \({\mathfrak g}\)-module L(F). The author considers the case where the Lie algebra \({\mathfrak g}_{\bar 0}\) of \({\mathfrak g}\) is semisimple and where E is the adjoint \({\mathfrak g}\)- module. Using the Weyl group W of \({\mathfrak g}_{\bar 0}\) he derives certain relations between matrix elements of such tensor operators. (Unfortunately, the author's statements concerning the action of W on \({\mathfrak g}\) and, more generally, on arbitrary \({\mathfrak g}\)-modules, are not correct. Nevertheless, I think his main results should be true.)
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 81T60
Mathematics Subject Classification ID: 17B15
zbMATH DE Number: 4142268
zbMATH Keywords: complex Lie superalgebra
zbMATH Keywords: tensor operator
zbMATH Keywords: relations between matrix elements
reviewed by: M. Scheunert
MaRDI profile type: Publication
cites work: The generalization of SU(3)-mass formulae for arbitrary reductive Lie algebras
cites work: Lie superalgebras
cites work: Q4061644
full work available at URL: https://doi.org/10.1007/bf00399969
OpenAlex ID: W2168628575
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description: scientific article; zbMATH DE number 4142268