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

TL;DR

This paper constructs specific simple G-C*-algebras for second countable locally compact groups, demonstrating cases where full and reduced crossed products coincide and differ, thus resolving longstanding open problems.

Contribution

It provides explicit examples of simple G-C*-algebras with coinciding full and reduced crossed products, addressing two open problems from 2002.

Findings

Constructed simple G-C*-algebras with coinciding full and reduced crossed products.

Developed G-equivariant representations on simple G-C*-algebras without the coincidence.

Resolved two open problems posed by Anantharaman-Delaroche in 2002.

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.