KMS States of Self-Similar k-Graph C*-Algebras

2018/05/22 by Li, Hui, Yang, Dilian
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1805.08366

Abstract

Let G be a countable discrete amenable group, and Λ be a strongly connected finite k-graph. If (G,Λ) is a pseudo free and locally faithful self-similar action which satisfies the finite-state condition, then the structure of the KMS simplex of the C*-algebra Ø_G,Λ associated to (G,Λ) is described: it is either empty or affinely isomorphic to the tracial state space of the C*-algebra of the periodicity group \Per_G,Λ of (G,Λ), depending on whether the Perron-Frobenius eigenvector of Λ preserves the G-action. As applications of our main results, we also exhibit several classes of important examples.

Related

• KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space
• Self-Similar k-Graph C*-Algebras
• C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states
• KMS states on the C*-algebras of finite graphs
• KMS states on C^*-algebras associated with self-similar sets