Hausdorff measures and KMS states
Copyright policy )Hausdorff measures and KMS states
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.
18 pages, 1 figure
Mathematics - Operator Algebras, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 46L40, 46L30, 37D35, 37B10, Operator Algebras (math.OA)
Mathematics - Operator Algebras, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 46L40, 46L30, 37D35, 37B10, Operator Algebras (math.OA)
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