scholarly journals Crossed product $C^*$-algebras by finite group actions with the tracial Rokhlin property

2011 ◽  
Vol 41 (6) ◽  
pp. 1755-1768 ◽  
Author(s):  
Dawn Archey
Keyword(s):  
Finite Group ◽  
Group Actions ◽  
Crossed Product ◽  
Finite Group Actions ◽  
C Algebras ◽  
Tracial Rokhlin Property

Crossed products by actions of finite groups with the Rokhlin property

2015 ◽  
Vol 26 (07) ◽  
pp. 1550042 ◽  
Author(s):  
Luis Santiago
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Group Actions ◽  
Crossed Product ◽  
Crossed Products ◽  
Finite Group Actions ◽  
C Algebras ◽  
Type Property ◽  
The Given

We introduce and study a Rokhlin-type property for actions of finite groups on (not necessarily unital) C*-algebras. We show that the corresponding crossed product C*-algebras can be locally approximated by C*-algebras that are stably isomorphic to closed two-sided ideals of the given algebra. We then use this result to prove that several classes of C*-algebras are closed under crossed products by finite group actions with this Rokhlin property.

scholarly journals The Tracial Class Property for Crossed Products by Finite Group Actions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Xinbing Yang ◽  
Xiaochun Fang
Keyword(s):  
Finite Group ◽  
Group Actions ◽  
Crossed Products ◽  
Finite Group Actions ◽  
Infinite Dimensional ◽  
A Finite Group ◽  
Tracial Rokhlin Property

We define the concept of tracial𝒞-algebra ofC*-algebras, which generalize the concept of local𝒞-algebra ofC*-algebras given by H. Osaka and N. C. Phillips. Let𝒞be any class of separable unitalC*-algebras. LetAbe an infinite dimensional simple unital tracial𝒞-algebra with the (SP)-property, and letα:G→Aut(A)be an action of a finite groupGonAwhich has the tracial Rokhlin property. ThenA  ×α  Gis a simple unital tracial𝒞-algebra.

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