Stable rank for crossed products by finite group actions with the weak tracial Rokhlin property

2024/07/13 by Fang, Xiaochun, Wang, Zhongli
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2407.09867

Abstract

Let A be an infinite-dimensional stably finite simple unital C*-algebra, let G be a finite group, and let α\colon G→ Aut(A) be an action of G on A which has the weak tracial Rokhlin property. We prove that if A has property (TM), then the crossed product A\rtimes_αG has property (TM). As a corollary, if A is an infinite-dimensional separable simple unital C*-algebra which has stable rank one and strict comparison, α\colon G→ Aut(A) is an action of a finite group G on A with the weak tracial Rokhlin property, then A\rtimes_αG has stable rank one.

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