Robertson, David

Rout, James

Sims, Aidan

2018-01

<p>We study the generalised Bunce-Deddens algebras and their Toeplitz extensions constructed by Kribs and Solel from a directed graph and a sequence ω of positive integers. We describe both of these C*-algebras in terms of novel universal properties, and prove uniqueness theorems for them; if ω determines an infinite supernatural number, then no aperiodicity hypothesis is needed in our uniqueness theorem for the generalised Bunce-Deddens algebra. We calculate the KMS states for the gauge action in the Toeplitz algebra when the underlying graph is finite. We deduce that the generalised Bunce-Deddens algebra is simple if and only if it supports exactly one KMS state, and this is equivalent to the terms in the sequence ω all being coprime with the period of the underlying graph.</p>

Bulletin of the Malaysian Mathematical Sciences Society, 41(1), p. 123-157

2180-4206

0126-6705

https://hdl.handle.net/1959.11/31862

Springer

KMS States on Generalised Bunce-Deddens Algebras and their Toeplitz Extensions

Journal Article

Publication