For any second countable locally compact group , we construct a simple -C*- algebra whose full and reduced crossed product norms coincide. We then construct its -equivariant representation on another simple -C*-algebra without the coincidence condition. This settles two problems posed by Anantharaman-Delaroche in 2002. Some constructions involve the Baire category theorem.
Cite this article
Yuhei Suzuki, Simple equivariant C*-algebras whose full and reduced crossed products coincide. J. Noncommut. Geom. 13 (2019), no. 4, pp. 1577–1585DOI 10.4171/JNCG/356