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On simple modules over conformal Galilei algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 218, no 10, 1885-1899 p.Article in journal (Refereed) Published
Abstract [en]

We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules over the conformal Galilei algebras. This can be viewed as an analogue of oscillator representations. We use oscillator representations to describe the structure of simple highest weight modules over conformal Galilei algebras. We classify simple weight modules with finite dimensional weight spaces over finite dimensional Heisenberg algebras and use this classification and properties of oscillator representations to classify simple weight modules with finite dimensional weight spaces over conformal Galilei algebras. 

Place, publisher, year, edition, pages
2014. Vol. 218, no 10, 1885-1899 p.
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Algebra and Logic
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URN: urn:nbn:se:uu:diva-228940DOI: 10.1016/j.jpaa.2014.02.012ISI: 000337928600010OAI: oai:DiVA.org:uu-228940DiVA: diva2:736930
Available from: 2014-08-11 Created: 2014-07-24 Last updated: 2017-12-05Bibliographically approved

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Mazorchuk, Volodymyr

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