Hausdorff measures and KMS states
Marius IonescuAlex Kumjian
46L4046L3037D3537B10Operator algebrasdynamical systemsKMS statesHausdorff measure
Given a compact metric space $X$ and a local homeomorphism $T:X\to X$ satisfying a local scaling property, we show that the Hausdorff measure on $X$ gives rise to a KMS state on the $C^{*}$-algebra naturally associated with the pair $(X,T)$ such that the inverse temperature coincides with the Hausdorff dimension. We prove that the KMS state is unique under some mild hypotheses. We then use our results to describe KMS states on Cuntz algebras, graph algebras, and certain $C^{*}$-algebras associated with fractafolds.
Indiana University Mathematics Journal
2013
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10.1512/iumj.2013.62.4904
10.1512/iumj.2013.62.4904
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Indiana Univ. Math. J. 62 (2013) 443 - 463
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