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On functors associated to a simple root
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. 314, no 1, 97-128 p.Article in journal (Refereed) Published
Abstract [en]

Associated to a simple root of a finite-dimensional complex semisimple Lie algebra, there are several endofunctors (defined by Arkhipov, Enright, Frenkel, Irving, Jantzen, Joseph, Mathieu, Vogan and Zuckerman) on the BGG category O. We study their relations, compute cohomologies of their derived functors and describe the monoid generated by Arkhipov's and Joseph's functors and the monoid generated by Irving's functors. It turns out that the endomorphism rings of all elements in these monoids are isomorphic. We prove that the functors give rise to an action of the singular braid monoid on the bounded derived category of O-0. We also use Arkhipov's, Joseph's and Irving's functors to produce new generalized tilting modules.

Place, publisher, year, edition, pages
2007. Vol. 314, no 1, 97-128 p.
Keyword [en]
lie algebra, category O, functor, translation twisting module
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-144543DOI: 10.1016/j.jalgebra.2007.03.015ISI: 000247710600005OAI: oai:DiVA.org:uu-144543DiVA: diva2:393791
Available from: 2011-02-01 Created: 2011-01-31 Last updated: 2011-02-01Bibliographically approved

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