KMS states of self-similar k-graph C*-algebras

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 OG,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 PerG,Λ of (G,Λ), depending on whether the Perron-Frobenius eigenvector of Λ is G-equivariant. As applications of our main results, we also exhibit several classes of important examples.