The tracial class property for crossed products by finite group actions
type: Item
instance of: scholarly article
title: The tracial class property for crossed products by finite group actions
zbMATH Open document ID: 1262.46046
DOI: 10.1155/2012/745369
author: Xinbing Yang
author: Xiaochun Fang
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: We define the concept of tracial \(\mathcal C\)-algebra of \(C^\ast\)-algebras, which generalizes the concept of local \(\mathcal C\)-algebra of \(C^\ast\)-algebras given by \textit{H. Osaka} and \textit{N. C. Phillips} [Math. Z. 270, No.~1--2, 19--42 (2012; Zbl 1244.46032)]. Let \(\mathcal C\) be any class of separable unital \(C^\ast\)-algebras. Let \(A\) be an infinite dimensional simple unital tracial \(\mathcal C\)-algebra with the (SP)-property, and let \(\alpha : G \rightarrow \text{Aut}(A)\) be an action of a finite group \(G\) on \(A\) which has the tracial Rokhlin property. Then \(A \times_\alpha G\) is a simple unital tracial \(\mathcal C\)-algebra.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 6134160
zbMATH Keywords: tracial \(\mathcal C\)-algebra
Wikidata QID: Q58696713
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/745369
OpenAlex ID: W2145855739
cites work: The tracial topological rank of \(C^*\)-algebras
cites work: Classification of simple \(C^*\)-algebras of tracial topological rank zero
cites work: Classification of simple \(C^{\ast}\)-algebras and higher dimensional noncommutative tori
cites work: The classification of certain non-simple \(C^*\)-algebras of tracial rank zero
cites work: Q5430226
cites work: On tracial approximation
cites work: Certain properties for crossed products by automorphisms with a certain non-simple tracial Rokhlin property
cites work: Outer conjugacy classes of automorphisms of factors
cites work: Stability for integer actions on UHF \(C^*\)-algebras
cites work: Classification of certain infinite simple \(C^*\)-algebras
cites work: The Rohlin property for shifts on UHF algebras and automorphisms of Cuntz algebras
cites work: The tracial Rokhlin property for actions of finite groups on C*-algebras
cites work: Crossed products by finite group actions with the Rokhlin property
cites work: The real rank zero property of crossed product
cites work: The Rokhlin property and the tracial topological rank
cites work: Stable and real rank for crossed products by automorphisms with the tracial Rokhlin property
cites work: The tracial rank for crossed products by finite group actions
cites work: An introduction to the classification of amenable \(C^*\)-algebras
cites work: Q4211799
description: scientific article; zbMATH DE number 6134160