Topological full groups arising from Cuntz and Cuntz-Toeplitz algebras and their crossed products

Abstract

In this paper, we investigate the topological full groups arising from the Cuntz and Cuntz-Toeplitz algebras and their crossed products with the Cartan subalgebras of Cuntz and Cuntz-Toeplitz algebras. We study the normal subgroups and abelianization of these groups and completely determine the KMS states of the reduced crossed products with respect to some canonical gauge actions.

33 pages(v1, v2) 29 pages(v3); typos corrected, reference added (v2); proof simplified, reference added(v3)