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

Let G be a countable discrete amenable group, and Lambda be a strongly connected finite k-graph. If (G, Lambda) 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 O-G,O- Lambda associated to (G, Lambda) is described: it is either empty or affinely isomorphic to the tracial state space of the C*-algebra of the periodicity group Per(G, Lambda) of (G, Lambda), depending on whether the Perron-Frobenius eigenvector of Lambda is G-equivariant. As applications of our main results, we also exhibit several classes of important examples. (C) 2019 Elsevier Inc. All rights reserved.