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Typical blocks of the category O for the queer Lie superalgebra
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Journal of Algebra and its Applications, ISSN 0219-4988, Vol. 6, no 5, 731-778 p.Article in journal (Refereed) Published
Abstract [en]

We study the category O for the queer Lie superalgebra q(n), and the corresponding block decomposition induced by infinitesimal central characters. In particular, we show that the so-called typical blocks correspond to standardly stratified algebras, in the sense of Cline, Parshall and Scott. By standard arguments for Lie algebras, modified to the superalgebra situation, we prove that these CPS-stratified algebras have finite finitistic dimension and the double centralizer property. Moreover, we prove that certain strongly typical blocks are equivalent. Finally, we generalize Kostant's Theorem to the q(n)-case and describe all typical q(2)-blocks.

Place, publisher, year, edition, pages
2007. Vol. 6, no 5, 731-778 p.
Keyword [en]
the queer Lie superalgebra q(n), standardly stratified algebra, quasi-hereditary algebra
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-95662ISI: 000250863400001OAI: oai:DiVA.org:uu-95662DiVA: diva2:169967
Available from: 2007-05-03 Created: 2007-05-03 Last updated: 2011-01-18Bibliographically approved
In thesis
1. On Stratified Algebras and Lie Superalgebras
Open this publication in new window or tab >>On Stratified Algebras and Lie Superalgebras
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis, consisting of three papers and a summary, studies properties of stratified algebras and representations of Lie superalgebras.

In Paper I we give a characterization when the Ringel dual of an SSS-algebra is properly stratified.

We show that for an SSS-algebra, whose Ringel dual is properly stratified, there is a (generalized) tilting module which allows one to compute the finitistic dimension of the SSS-algebra, and moreover, it gives rise to a new covariant Ringel-type duality.

In Paper II we give a characterization of standardly stratified algebras in terms of certain filtrations of (left or right) projective modules, generalizing the corresponding theorem of V. Dlab. We extend the notion of Ringel duality to standardly stratified algebras and estimate their finitistic dimension in terms of endomorphism algebras of standard modules.

Paper III deals with the queer Lie superalgebra and the corresponding BGG-category O. We show that the typical blocks correspond to standardly stratified algebras, and we generalize Kostant's Theorem to the queer Lie superalgebra.

Place, publisher, year, edition, pages
Uppsala: Matematiska institutionen, 2007. 17 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 48
Keyword
Algebra and geometry, Stratified algebras, Lie Superalgebras, Properly stratified algebras, Quasi-hereditary algebras, the queer Lie superalgebra, Kostant's Theorem, Algebra och geometri
Identifiers
urn:nbn:se:uu:diva-7781 (URN)978-91-506-1927-0 (ISBN)
Public defence
2007-05-29, MIC2247, House 2, Polacksbacken, Uppsala, 13:15
Opponent
Supervisors
Available from: 2007-05-03 Created: 2007-05-03Bibliographically approved

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