Support varieties for transporter category algebras

Details Support varieties for transporter category algebras Support varieties for transporter category algebras

2011-05-24

arxiv.org/abs/1105.4731v3

Mathematics

Group Theory

22 pages. Removed some small errors. Added a Lemma 2.3.2 and 2 new references on Gorenstein skew group algebras

Scientific paper

Let G be a finite group. Over any finite G-poset P we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter category is the Borel construction on the G-space BP, while the k-category algebra of the transporter category is the (Gorenstein) skew group algebra on the G-incidence algebra kP. We introduce a support variety theory for the category algebras of transporter categories. It extends Carlson's support variety theory on group cohomology rings to equivariant cohomology rings. In the mean time it provides a class of (usually non selfinjective) algebras to which Snashall-Solberg's (Hochschild) support variety theory applies. Various properties will be developed. Particularly we establish a Quillen stratification for modules.

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