Partial tensor-product functors and crossed-product functors

TL;DR

This paper characterizes specific crossed-product functors for discrete groups using tensor product techniques, clarifying their relationships and properties within operator algebra theory.

Contribution

It provides an explicit description of the minimal exact and maximal injective crossed-product functors for discrete groups, establishing their dominance relation.

Findings

Explicit description of minimal exact correspondence crossed-product functor

Explicit description of maximal injective crossed-product functor

Demonstration that the former dominates the latter

Abstract

For a given discrete group $G$, we apply results of Kirchberg on exact and injective tensor products of $C^*$-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.