Freeness of actions of finite groups on C*-algebras

Abstract

We describe some of the forms of freeness of group actions on noncommutative C*-algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths, weaknesses, applications, and relationships to each other. The properties discussed include the Rokhlin property, K-theoretic freeness, the tracial Rokhlin property, pointwise outerness, saturation, hereditary saturation, and the requirement that the strong Connes spectrum be the entire dual.

arXiv comment40 pages; AMSLaTeX. Submitted to the proceedings of the workshop "Operator Structures and Dynamical Systems", Leiden, July 2008

References in corpus (3)

• The ideal structure of reduced crossed products
• Crossed product C*-algebras by finite group actions with the projection free tracial Rokhlin property
• Crossed products by finite group actions with the Rokhlin property

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• Noncommutative Coverings of Quantum Tori
• Anticommutation in the Presentations of Theta-Deformed Spheres
• Invariants in Noncommutative Dynamics
• Part III, Free Actions of Compact Quantum Groups on C*-Algebras
• Compact Group Actions with the Tracial Rokhlin Property
• Triviality of Equivariant Maps in Crossed Products and Matrix Algebras