C*-envelopes and the Hao-Ng isomorphism for discrete groups

TL;DR

This paper proves the Hao-Ng isomorphism for reduced crossed products with all discrete groups using non-selfadjoint techniques, and extends results to full crossed products with hyperrigid correspondences.

Contribution

It establishes the Hao-Ng isomorphism for reduced crossed products for all discrete groups and extends the result to full crossed products under hyperrigidity conditions.

Findings

Hao-Ng isomorphism holds for reduced crossed products with all discrete groups.

An analogous result is shown for full crossed products with hyperrigid correspondences.

C*-envelope calculation is key to deriving these results.

Abstract

Using non-selfadjoint techniques, we establish the Hao-Ng isomorphism for the reduced crossed product and all discrete groups. For the full crossed product an analogous result holds for all discrete groups but the C*-correspondences involved have to be hyperrigid. These results are obtained by calculating the C*-envelope of the reduced crossed product of an operator algebra by a discrete group.