CROSSED PRODUCT C~*-ALGEBRAS BY FINITE GROUP ACTIONS WITH THE TRACIAL ROKHLIN PROPERTY

摘要

Let A be a stably finite simple unital C~*- algebra, and suppose a is an action of a finite group G with the tracial Rokhlin property. Suppose further A has real rank zero and the order on projections over A is determined by traces. Then the crossed product C~*-algebra C~*(G,A,α) also has real rank zero and order on projections over A is determined by traces. Moreover, if A also has stable rank one, then C~*(G,A,α) also has stable rank one.