Certain tracially nuclear dimensional for certain crossed product \rm C^*-algebras

2022/10/13 by Qingzhai Fan, Fan, Qingzhai, Wang, Jiahui
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2210.07008

openalex publication_date 2022/10/13 · openalex created_date 2022/10/15 · openalex updated_date 2026/07/28

Abstract

Let Ω be a class of unital \rm C^*-algebras which have the second type tracial nuclear dimensional at moat n (or have tracial nuclear dimensional at most n). Let A be an infinite dimensional unital simple \rm C^*-algebra such that A is asymptotical tracially in Ω. Then \rm T²dim_nuc(A)≤ n (or \rm Tdim_nuc(A)≤ n). As an application, let A be an infinite dimensional simple separable amenable unital \rm C^*-algebra with \rm T²dim_nuc(A)≤ n (or \rm Tdim_nuc(A)≤ n). Suppose that α:G→ \rm Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property. Then \rm T²dim_nuc(\rm C^*(G, A,α))≤ n (or \rm Tdim_nuc (\rm C^*(G, A,α))≤ n).

Related

• Certain properties of generalized tracially approximated C*-algebras
• Nuclear dimension for an inclusion of unital C*-algebras
• Existence of the Matui-Sato tracial Rokhlin property
• Tracial approximation in simple C*-algebras
• Some properties for certain generalized tracial approximated \rm C^*-algebras