Year: 1985
Type: article
Abstract: In [11] G. G. Kasparov defined the “operatorK-functor”KK(A, B)associated with the gradedC*-algebrasAandB. If the algebrasAandBare trivially graded andAis nuclear he proves six term exact sequence theorems. He asks whether this extends to the graded case. Here we prove such “six-term exact sequence” results in the graded case. Our proof does not use nuclearity of the algebraA. This condition is replaced by a completely positive lifting condition (Theorem 1.1). Using our result we may extend the results by M. Pimsner and D. Voiculescu on theKgroups of crossed products by free groups toKKgroups [15]. We give however a different way of computing these groups using the equivariantKK-theory developed by G. G. Kasparov in [12]. This method also allows us to compute the KK groups of crossed products byPSL2(Z).
Source: Canadian Journal of Mathematics
Author: George Skandalis
Institutions: Queen's University, Queens University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2069738138