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

Title
KMS States on Generalised Bunce-Deddens Algebras and their Toeplitz Extensions
Publication Date
2018-01
Author(s)
Robertson, David
( author )
OrcID: https://orcid.org/0000-0002-0425-4775
Email: drober54@une.edu.au
UNE Id une-id:drober54
Rout, James
Sims, Aidan
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Springer
Place of publication
Germany
DOI
10.1007/s40840-015-0244-8
UNE publication id
une:1959.11/31862
Abstract

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.

Link
Citation
Bulletin of the Malaysian Mathematical Sciences Society, 41(1), p. 123-157
ISSN
2180-4206
0126-6705
Start page
123
End page
157

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