Hausdorff Measures and KMS States

2010/02/03 by Ionescu, Marius, Kumjian, Alex · 1 citation
#37B10 #37D35 #46L30 #46L40 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1002.0790

Abstract

Given a compact metric space X and a local homeomorphism T:X→ 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.

Cited by

• A panoramic view of groupoids and MRAs

Related

• Generalized gauge actions on k-graph C^*-algebras: KMS states and Hausdorff structure
• KMS states on C*-algebras associated to local homeomorphisms
• KMS states on C^*-algebras associated to a family of *-commuting\n local homeomorphisms
• On the C*-algebra of a locally injective surjection and its KMS states
• KMS states on C*-algebras associated to expansive maps