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Classification of Simple Weight Modules Over the 1-Spatial Ageing Algebra
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2015 (English)In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 18, no 2, 381-395 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we use Block's classification of simple modules over the first Weyl algebra to obtain a complete classification of simple weight modules, in particular, of Harish-Chandra modules, over the 1-spatial ageing algebra . Most of these modules have infinite dimensional weight spaces and so far the algebra is the only Lie algebra having simple weight modules with infinite dimensional weight spaces for which such a classification exists. As an application we classify all simple weight modules over the (1+1)-dimensional space-time Schrodinger algebra that have a simple -submodule thus constructing many new simple weight S-modules.

Place, publisher, year, edition, pages
2015. Vol. 18, no 2, 381-395 p.
Keyword [en]
Weight module, Schrodinger algebra, Ageing algebra, Highest weight module
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URN: urn:nbn:se:uu:diva-252178DOI: 10.1007/s10468-014-9499-2ISI: 000352969700007OAI: oai:DiVA.org:uu-252178DiVA: diva2:810158
Available from: 2015-05-06 Created: 2015-05-04 Last updated: 2015-05-06Bibliographically approved

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Algebra and Geometry
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Algebras and Representation Theory

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