Articles

CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY

  • Qingzhai Fan ,
  • Xiaochun Fang
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  • 1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China;
    2. Department of Mathematics, Tongji University, Shanghai 200092, China

Received date: 2017-05-30

  Revised date: 2017-08-08

  Online published: 2018-06-25

Supported by

The first author is supported by NSFCs (11501357, 11571008).

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.

Cite this article

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 . DOI: 10.1016/S0252-9602(18)30787-2

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