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arXiv · 1002.0790

Hausdorff Measures and KMS States

Marius Ionescu·Alex Kumjian
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Abstract

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 to 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 hypothesis. We use our results to describe KMS states on Cuntz algebras, graph algebras, and $C^{*}$-algebras on fractafolds.

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BibTeXRIS

Marius Ionescu, Alex Kumjian. 2012-07-27. Hausdorff Measures and KMS States. https://arxiv.org/abs/1002.0790

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