数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (3): 829-842.doi: 10.1016/S0252-9602(18)30787-2

• 论文 • 上一篇    下一篇

CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY

范庆斋1, 方小春2   

  1. 1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China;
    2. Department of Mathematics, Tongji University, Shanghai 200092, China
  • 收稿日期:2017-05-30 修回日期:2017-08-08 出版日期:2018-06-25 发布日期:2018-06-25
  • 作者简介:Qingzhai Fan,E-mail:fanqingzhai@fudan.edu.cn,qzfan@shmtu.edu.cn;Xiaochun Fang,E-mail:xfang@mail.tongji.edu.cn
  • 基金资助:

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

CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY

Qingzhai Fan1, Xiaochun Fang2   

  1. 1. Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China;
    2. Department of Mathematics, Tongji University, Shanghai 200092, China
  • Received:2017-05-30 Revised:2017-08-08 Online:2018-06-25 Published:2018-06-25
  • Supported by:

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

摘要:

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.

关键词: C*-algebras, Rokhlin property, crossed product C*-algebra

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