Classification of irreducible integrable modules for toroidal Lie algebras with finite dimensional weight spaces
type: Item
instance of: scholarly article
title: Classification of irreducible integrable modules for toroidal Lie algebras with finite dimensional weight spaces
zbMATH Open document ID: 1106.17001
published in: Journal of Algebra
publication date: 2004-09-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0209060
review text: In [J. Algebra 246, No. 1, 215--225 (2001; Zbl 0994.17002)] the author classified all integrable modules with finite-dimensional weight spaces and with the trivial action of the center over toroidal Lie algebras. In the present paper this result is extended to the classification of all integrable modules with finite-dimensional weight spaces over toroidal Lie algebras.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 2102481
zbMATH Keywords: toroidal Lie algebra
zbMATH Keywords: integrable module
zbMATH Keywords: weight space
author: S. Eswara Rao
MaRDI profile type: Publication
OpenAlex ID: W1974603011
Wikidata QID: Q115351738
arXiv ID: math/0209060
cites work: Representations of twisted multi-loop Lie algebras.
cites work: Irreducible representations for toroidal Lie algebras
cites work: Enveloping algebras and representations of toroidal Lie algebras
cites work: Quantum tori and the structure of elliptic quasi-simple Lie algebras
cites work: Integrable representations of affine Lie-algebras
cites work: New unitary representations of loop groups
cites work: Iterated loop modules and a filteration for vertex representation of toroidal Lie algebras
cites work: Classification of irreducible integrable modules for multi-loop algebras with finite-dimensional weight spaces
cites work: Irreducible representations for toroidal Lie-algebras
cites work: Vertex representations for \(n\)-toroidal Lie algebras and a generalization of the Virasoro algebra
cites work: Q3838046
cites work: Irreducible non-dense \(A_ 1^{(1)}\)-modules
cites work: Introduction to Lie Algebras and Representation Theory
cites work: Q4040877
cites work: Toroidal Lie algebras and vertex representations
cites work: Q3129438
cites work: On the polynomial representations of current algebras
DOI: 10.1016/J.JALGEBRA.2004.03.016
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