Integrable representations for generalized Virasoro-toroidal Lie algebras.
type: Item
instance of: scholarly article
title: Integrable representations for generalized Virasoro-toroidal Lie algebras.
zbMATH Open document ID: 1037.17029
published in: Journal of Algebra
publication date: 2004-01-14T00:00:00Z
review text: Let \(V\) be an irreducible integrable module over a generalized Virasoro-toroidal Lie algebra \(\mathfrak{g}\). In this paper it is shown that if \(M\) has finite-dimensional weight spaces and a non-zero central charge, then \(M\cong L(\Lambda)\otimes \overline{M}\), where \(L(\Lambda)\) is an irreducible highest (or lowest) weight module for an appropriate affine Lie algebra, associated with \(\mathfrak{g}\), and \(\overline{M}\) is an irreducible module over the centrally extended subalgebra of full derivations of \(\mathfrak{g}\) with finite-dimensional weight spaces and the same central charge.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 2026930
zbMATH Keywords: integrable representation
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: toroidal algebra
zbMATH Keywords: irreducible representation
zbMATH Keywords: weight
author: Cuipo Jiang
author: Daoji Meng
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.06.006
OpenAlex ID: W2074409243
Wikidata QID: Q115351814
cites work: Q3755625
cites work: Irreducible representations for toroidal Lie algebras
cites work: Enveloping algebras and representations of toroidal Lie algebras
cites work: Principal vertex operator representations for toroidal Lie algebras
cites work: An extension of the Korteweg-de Vries hierarchy arising from a representation of a toroidal Lie algebra
cites work: Integrable representations of affine Lie-algebras
cites work: Borel subalgebras and categories of highest weight modules for toroidal Lie algebras
cites work: Classification of irreducible integrable modules for toroidal Lie algebras with finite dimensional weight spaces
cites work: Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
cites work: Basic representations of affine Lie algebras and dual resonance models
cites work: Q3792881
cites work: Irreducible representations of Virasoro-toroidal Lie algebras
cites work: Vertex operators arising from the homogeneous realization for \(\widehat{\text{gl}}_N\)
cites work: Vertex representations for the \(\nu +1\)-toroidal Lie algebra of type \(B_l\).
cites work: Q3693664
cites work: A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
cites work: The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
cites work: Toroidal Lie algebras and vertex representations
cites work: Vertex operator representations for toroidal lie algebra of typeBl
cites work: Principal construction of the toroidal Lie algebra of type \(A_1\)
cites work: Q4804639
cites work: Vertex Operator Construction for the Toroidal Lie Algebra of TypeF4
DOI: 10.1016/J.JALGEBRA.2003.06.006
description: scientific article; zbMATH DE number 2026930