Irreducible representations of the Lie-algebra of the diffeomorphisms of a \(d\)-dimensional torus
type: Item
instance of: scholarly article
title: Irreducible representations of the Lie-algebra of the diffeomorphisms of a \(d\)-dimensional torus
zbMATH Open document ID: 0902.17012
published in: Journal of Algebra
publication date: 1996-10-31T00:00:00Z
review text: This paper discusses the irreducibility of certain modules associated with the Lie algebra of diffeomorphisms of the \(d\)-dimensional torus. First, the paper regards the above diffeomorphisms as derivations of a Laurent polynomial ring \(A\) in \(d\) variables and recalls a functor from the \(gl_d\)-modules to the (Der \(A)\)-modules (where \(gl_d\) is the Lie algebra of \(d \times d\) complex matrices). Then, the paper shows that the image of a finite-dimensional irreducible \(gl_d\)-module is most often irreducible. The only exceptions are fundamental modules and one dimensional modules. The paper is motivated by some problems related to the Virasoro algebra.
reviewed by: Marco Modugno
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 922311
zbMATH Keywords: irreducibility
zbMATH Keywords: Lie algebra of diffeomorphisms
author: S. Eswara Rao
MaRDI profile type: Publication
full work available at URL: jabr.1996.0177
OpenAlex ID: W2112414626
Wikidata QID: Q115396096
DOI: 10.1006/JABR.1996.0177
description: scientific article; zbMATH DE number 922311