Indecomposable representations of the Lie algebra of derivations for \(d\)-torus
type: Item
instance of: scholarly article
title: Indecomposable representations of the Lie algebra of derivations for \(d\)-torus
zbMATH Open document ID: 1193.17006
author: Shaobin Tan
author: Bo Zeng
author: Haifeng Lian
published in: Science China. Mathematics
publication date: 2010-04-13T00:00:00Z
review text: There is a classical functor from the category of finite-dimensional \(\mathfrak{gl}_d\)-modules to the category of modules over the Lie algebra of derivations of the \(d\)-dimensional torus, constructed by \textit{T. A. Larsson} in [Conformal fields: a class of representations of \(\text{Vect}(N)\)'', Int. J. Mod. Phys. A 7, No. 26, 6493--6508 (1992; Zbl 0972.17502)]. In the paper under review the authors study the images of indecomposable finite-dimensional \(\mathfrak{gl}_d\)-modules under this functor. They show that these images are always indecomposable and most often uniserial. In the case when the module is uniserial, its unique composition series is described in details.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 5692414
zbMATH Keywords: torus
zbMATH Keywords: Lie algebra of derivations
zbMATH Keywords: representation
zbMATH Keywords: composition series
Wikidata QID: Q115378339
MaRDI profile type: Publication
full work available at URL: s11425-009-0034-6
OpenAlex ID: W2015498947
cites work: Q3820760
cites work: CONFORMAL FIELDS: A CLASS OF REPRESENTATIONS OF Vect(N)
cites work: Representations of the Lie algebra of derivations for quantum torus
cites work: Classification of the indecomposable bounded admissible modules over the Virasoro Lie algebra with weightspaces of dimension not exceeding two
cites work: Classification of Harish-Chandra modules over the Virasoro Lie algebra
cites work: Classification of simple weight Virasoro modules with a finite-dimensional weight space
cites work: Introduction to Lie Algebras and Representation Theory
cites work: Algebras of diffeomorphisms of the N-torus
cites work: Representations of Witt algebras
cites work: Irreducible representations of the Lie-algebra of the diffeomorphisms of a \(d\)-dimensional torus
cites work: Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus
cites work: Classification of irreducible integrable representations for the full toroidal Lie algebras
cites work: Q3735909
DOI: 10.1007/S11425-009-0034-6
description: scientific article; zbMATH DE number 5692414