Bouc, Serge Hochschild constructions for Green functors. (English) Zbl 1070.16010 Commun. Algebra 31, No. 1, 403-436 (2003). Let \(G\) be a finite group and let \(R\) be a commutative ring. The Hochschild cohomology ring \(HH^*(RG,RG)\) has an additive decomposition \(HH^*(RG,RG)=\bigoplus_{x\in X}H^*(C_G(x),R)\) where \(X\) is a transversal for the conjugacy classes of \(G\) and where \(H^*(C_G(x),R)\) denotes the cohomology ring of the group \(C_G(x)\), for \(x\in X\). S. F. Siegel and S. J. Witherspoon [Proc. Lond. Math. Soc., III. Ser. 79, No. 1, 131-157 (1999; Zbl 1044.16005)] have computed how the product in \(HH^*(RG,RG)\) is reflected by this decomposition. In the paper under review, the author shows that their result is a special case of a more general construction for Green functors. Reviewer: Burkhard Külshammer (Jena) Cited in 12 Documents MSC: 16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) 19A22 Frobenius induction, Burnside and representation rings 20J06 Cohomology of groups 20C05 Group rings of finite groups and their modules (group-theoretic aspects) 16S34 Group rings Keywords:group cohomology; Hochschild cohomology; Mackey functors; Green functors, Mackey algebras; Burnside rings Citations:Zbl 1044.16005 PDFBibTeX XMLCite \textit{S. Bouc}, Commun. Algebra 31, No. 1, 403--436 (2003; Zbl 1070.16010) Full Text: DOI References: [1] Bouc S., Lecture Notes in Mathematics 1671 (1997) [2] DOI: 10.1090/S0002-9939-97-03727-1 · Zbl 0865.18005 · doi:10.1090/S0002-9939-97-03727-1 [3] DOI: 10.1007/PL00000389 · Zbl 0872.16004 · doi:10.1007/PL00000389 [4] DOI: 10.2307/1970343 · Zbl 0131.27302 · doi:10.2307/1970343 [5] DOI: 10.1112/S0024611599011958 · Zbl 1044.16005 · doi:10.1112/S0024611599011958 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.