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Serre Functors for Lie Algebras and Superalgebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2012 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 62, no 1, 47-75 p.Article in journal (Refereed) Published
Abstract [en]

We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category O associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to classical Lie superalgebras in many cases. Along the way we prove that category O and its parabolic generalizations for classical Lie superalgebras are categories with full projective functors. As an application we prove that in many cases the endomorphism algebra of the basic projective-injective module in (parabolic) category O for classical Lie superalgebras is symmetric. As a special case we obtain that in these cases the algebras describing blocks of the category of finite dimensional modules are symmetric. We also compute the latter algebras for the superalgebra q(2).

Place, publisher, year, edition, pages
2012. Vol. 62, no 1, 47-75 p.
Keyword [en]
Lie superalgebra, module, Harish-Chandra bimodule, Serre functor, quiver, category O
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-259782ISI: 000308256000002OAI: oai:DiVA.org:uu-259782DiVA: diva2:845437
Funder
Swedish Research Council
Available from: 2015-08-11 Created: 2015-08-11 Last updated: 2017-12-04Bibliographically approved

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Mazorchuk, Volodymyr

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