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Characterization of Simple Highest Weight Modules
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 56, no 3, 606-614 p.Article in journal (Refereed) Published
Abstract [en]

We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra, and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro algebras and for Heisenberg algebras.

Place, publisher, year, edition, pages
2013. Vol. 56, no 3, 606-614 p.
Keyword [en]
Lie algebra, highest weight module, triangular decomposition, locally nilpotent action
National Category
URN: urn:nbn:se:uu:diva-207499DOI: 10.4153/CMB-2011-199-5ISI: 000323296400018OAI: oai:DiVA.org:uu-207499DiVA: diva2:648905
Available from: 2013-09-17 Created: 2013-09-16 Last updated: 2013-09-17Bibliographically approved

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Mazorchuk, Volodymyr
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