Hausdorff Measures and KMS States

Details Hausdorff Measures and KMS States Hausdorff Measures and KMS States

2010-02-03

arxiv.org/abs/1002.0790v2

Mathematics

Operator Algebras

12 pages, 1 figure

Scientific paper

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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