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

Abstract

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 ${Ø}_{G,\Lambda }$ 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 $\Per_{G,Λ}$ of $(G,\Lambda )$, depending on whether the Perron-Frobenius eigenvector of $\Lambda$ preserves the $G$-action. As applications of our main results, we also exhibit several classes of important examples.

34 pages

References in corpus (4)

• Equilibrium states on operator algebras associated to self-similar actions of groupoids on graphs
• Self-Similar $k$-Graph C*-Algebras
• Cartan Subalgebras of Topological Graph Algebras and k-Graph C*-algebras
• Boundary Quotient C*-algebras of Products of Odometers