The Tracial Class Property for Crossed Products by Finite Group Actions

Abstract EN

We define the concept of tracial ?-algebra of C*-algebras, which generalize the concept of local ?-algebra of C*-algebras given by H.

Osaka and N.

C.

Phillips.

Let ? be any class of separable unital C*-algebras.

Let A be an infinite dimensional simple unital tracial ?-algebra with the (SP)-property, and let α:G→Aut(A) be an action of a finite group G on A which has the tracial Rokhlin property.

Then A ×α G is a simple unital tracial ?-algebra.