2011/05/24 by Fei Xu, Xu, Fei
Mathematics · #16E40 #16P40 #20C05 #20J06 #55N25 #57S17 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AT #math.GR #math.RA #math.RT #msc:16E40 #msc:16P40 #msc:20C05 #msc:20J06 #msc:55N25 #msc:57S17
paper · pdf · doi:10.48550/arxiv.1105.4731
22 pages. Removed some small errors. Added a Lemma 2.3.2 and 2 new references on Gorenstein skew group algebras
openalex publication_date 2011/05/24 · arxiv created 2011/08/26 · arxiv updated 2011/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.