Support varieties for transporter category algebras
详细信息 查看全文
文摘
Let be a finite group. Over any finite -poset we may define a transporter category as the corresponding Grothendieck construction. The classifying space of the transporter category is the Borel construction on the -space , while the -category algebra of the transporter category is the (Gorenstein) skew group algebra on the -algebra .
We introduce a support variety theory for the category algebras of transporter categories. It extends Carlson鈥檚 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鈥檚 (Hochschild) support variety theory applies. Various properties will be developed. Particularly we establish a Quillen stratification for modules.