Partial tensor-product functors and crossed-product functors

Abstract

For a given discrete group $G$, we apply results of Kirchberg on exact and injective tensor products of $C^{\ast }$-algebras to give an explicit description of the minimal exact correspondence crossed-product functor and the maximal injective crossed-product functor for $G$ in the sense of Buss, Echterhoff and Willett. In particular, we show that the former functor dominates the latter.

9 pages, minor corrections. To appear in Proc. Amer. Math. Soc