Minimal index of a C*-crossed product by a finite group

摘要

Let A x(alpha) G be the C*-crossed product of a simple unital C*-algebra A by a finite group G. In this paper we show that the canonical conditional expectation from A x(alpha) G to A has the minimal index if A x(alpha) G is simple. It is also proved that if alpha is an outer action, then the canonical one is the unique conditional expectation of index-finite type from A x(alpha) G to A, while there are infinitely many conditional expectations when a nontrivial subgroup of G acts innerly on A. [References: 13]