The tracial Rokhlin property for actions of finite groups on C*-algebras

By Christopher Phillips. 2006

105 citations recorded by the source corpus.

We define ``tracial'' analogs of the Rokhlin property for actions of finite groups, approximate representability of actions of finite abelian groups, and approximate innerness. We prove the following four analogs of related ``nontracial'' results. $\bullet$ The crossed product of an infinite dimensional simple separable unital C*-algebra with tracial rank zero by an action of a finite group with the tracial Rokhlin property again has tracial rank zero. $\bullet$ An outer action of a finite abelian group on an infinite dimensional simple separable unital C*-algebra has the tracial Rokhlin property if and only if its dual is tracially approximately representable, and is tracially approximately representable if and only if its dual has the tracial Rokhlin property. $\bullet$ If a strongly tracially approximately inner action of a finite cyclic group on an infinite dimensional simple separable unital C*-algebra has the tracial Rokhlin property, then it is tracially approximately representable. $\bullet$ An automorphism of an infinite dimensional simple separable unital C*-algebra $A$ with tracial rank zero is tracially approximately inner if and only if it is the identity on $K_0 (A)$ mod infinitesimals.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/58523c616f6b697ad88b4a6ae3c908ffb49ef867

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

  1. G'abor Szab'o
  2. Jianchao Wu
  3. J. Zacharias
  4. W. Winter
  5. Eusebio Gardella

In Geometry and Topology

  1. Jianchao Wu
  2. G'abor Szab'o
  3. J. Zacharias

In Mathematical Physics

  1. G'abor Szab'o
  2. Jianchao Wu
  3. J. Zacharias
  4. W. Winter
  5. David Kerr
  6. Eusebio Gardella
  7. Aaron Tikuisis

Citations in the corpus