2022/04/07 by Massoud Amini, Nasser Golestani, Amini, Massoud +5
Materials Science · Mathematics · #46L05 #46L40 #46L55 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Organic and Molecular Conductors Research
paper · pdf · doi:10.48550/arxiv.2204.03615
openalex publication_date 2022/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that if A is a simple (not necessarily unital) tracially Z-absorbing C*-algebra and α\colon G → Aut (A) is an action of a finite group G on A with the weak tracial Rokhlin property, then the crossed product C^*(G, A,α) and the fixed point algebra Aα are simple and tracially Z-absorbing, and they are Z-stable if, in addition, A is separable and nuclear. The same conclusion holds for all intermediate C*-algebras of the inclusions Aα⊆ A and A ⊆ C^*(G, A,α). We prove that if A is a simple tracially Z-absorbing C*-algebra, then, under a finiteness condition, the permutation action of the symmetric group Sm on the minimal m-fold tensor product of A has the weak tracial Rokhlin property. We define the weak tracial Rokhlin property for automorphisms of simple C*-algebras and we show that -- under a mild assumption -- (tracial) Z-absorption is preserved under crossed products by such automorphisms.