CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY

doi:10.1016/S0252-9602(18)30787-2

Abstract

Abstract:

We introduce a special tracial Rokhlin property for unital C^*-algebras. Let A be a unital tracial rank zero C^*-algebra (or tracial rank no more than one C^*-algebra). Suppose that α:G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C^*-algebra. Then, the crossed product C^*-algebra C^*(G, A, α) has tracia rank zero (or has tracial rank no more than one). In fact, we get a more general results.

Key words: C^*-algebras, Rokhlin property, crossed product C^*-algebra

Qingzhai Fan, Xiaochun Fang. CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY[J].Acta mathematica scientia,Series B, 2018, 38(3): 829-842.

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