Simple equivariant C*-algebras whose full and reduced crossed products coincide

Abstract

For any second countable locally compact group G, we construct a simple G-C*-algebra whose full and reduced crossed product norms coincide. We then construct its G-equivariant representation on another simple G-C*-algebra without the coincidence condition. This settles two problems posed by Anantharaman-Delaroche in 2002. Some constructions involve the Baire category theorem.

6 pages, minor (non-mathematical) revision, to appear in Journal of Noncommutative Geometry

Cited by in corpus (6)

• On characterizations of amenable C*-dynamical systems and new examples
• Equivariant ${\mathcal{O}}_2$-absorption theorem for exact groups
• Non-amenable tight squeezes by Kirchberg algebras
• The approximation property and exactness of locally compact groups
• Crossed product splitting of intermediate operator algebras via 2-cocycles
• Amenable actions on ill-behaved simple C*-algebras