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Classification of simple weight Virasoro modules with a finite-dimensional weight space
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 307, no 1, 209-214 p.Article in journal (Refereed) Published
Abstract [en]

We show that the support of a simple weight module over the Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all non-trivial weight spaces of such module are infinite-dimensional. As a corollary we obtain that every simple weight module over the Virasoro algebra, having a non-trivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either a simple highest or lowest weight module or a simple module from the intermediate series). This implies positive answers to two conjectures about simple pointed and simple mixed modules over the Virasoro algebra.

Place, publisher, year, edition, pages
2007. Vol. 307, no 1, 209-214 p.
Keyword [en]
Virasoro algebra, Weight module, Simple module, Support
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-22124DOI: 10.1016/j.jalgebra.2006.05.007ISI: 000246418300011OAI: oai:DiVA.org:uu-22124DiVA: diva2:49897
Available from: 2007-01-10 Created: 2007-01-10 Last updated: 2017-12-07Bibliographically approved

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Mazorchuk, Volodymyr

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