IUMJ

Title: Hausdorff measures and KMS states

Authors: Marius Ionescu and Alex Kumjian

Issue: Volume 62 (2013), Issue 2, 443-463

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 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.