Uniform property Γ for Crossed products by group actions with the Rokhlin-type properties

2024/12/13 by Fang, Xiaochun, Tian, Haotian
#FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L55 #Secondary 46L35

paper · doi:10.48550/arxiv.2412.10486

Abstract

In this paper, let A be a unital separable simple infinite dimensional C*-algebra which has uniform property Γ. Let α\colon G→ Aut(A) be an action of a finite group which has the weak tracial Rokhlin property. Then we prove that the crossed product A\rtimes_αG and fixed point algebra A^α have uniform property Γ. Let α\colon G→ Aut(A) be an action of a second-countable compact group which has the tracial Rokhlin property with comparison. Then we prove that the crossed product A\rtimes_αG and fixed point algebra A^α have uniform property Γ.

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