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Some homological properties of the category O
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Pacific Journal of Mathematics, ISSN 0030-8730, E-ISSN 1945-5844, Vol. 232, no 2, 313-341 p.Article in journal (Refereed) Published
Abstract [en]

In the first part of this paper the projective dimension of the structural modules in the BGG category O is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an explicit conjecture relating the result to Lusztig's a-function is formulated ( and proved for type A). The second part deals with the extension algebra of Verma modules. It is shown that this algebra is in a natural way Z(2)-graded and that it has two Z-graded Koszul subalgebras. The dimension of the space Ext(1) into the projective Verma module is determined. In the last part several new classes of Koszul modules and modules, represented by linear complexes of tilting modules, are constructed.

Place, publisher, year, edition, pages
2007. Vol. 232, no 2, 313-341 p.
Keyword [en]
category O, projective dimension, tilting module, cell, linear complex, Koszul duality
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-113445ISI: 000251564200006OAI: oai:DiVA.org:uu-113445DiVA: diva2:290839
Available from: 2010-01-28 Created: 2010-01-28 Last updated: 2017-12-12Bibliographically approved

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