\(C^*\)-algèbres de Hopf et théorie de Kasparov équivariante. (Hopf \(C^*\)-algebras and equivariant Kasparov theory)
The authors define a concept of coaction of a Hopf \(C^*\)-algebra S on a pair of \(C^*\)-algebras (A,B) and generalise for the triple of the type (S,A,B) the Kasparov construction corresponding to the case of \(S=C_ 0(G)\), G being a locally compact group. So, an S-equivariant Kasparov theory group \(KK_ S(A,B)\) is obtained. Moreover, the Kasparov product is generalised to that setting, a natural isomorphism of the groups \(KK_ G(A,B)\) and \(KK_{C^*(G)}(A\times G,B\times G)\) is given and, for a discrete amenable group \(\Gamma\), the half-exactness of the functors \(KK_{\Gamma}(.,D)\) and \(KK_{\Gamma}(D,.)\) is proved.
scientific article; zbMATH DE number 4119008
scientific article