KMS STATES FOR QUASI-FREE ACTIONS ON FINITE-GRAPH ALGEBRAS

Given a graph E and a labeling map omega, we consider the quasi-free action alpha(omega) of R on the graph algebra C* (E). For a finite graph E, we give a complete characterization of all KMS beta states of a graph algebra in terms of a polyhedral set in RE0. This characterization allows us to generalize the results of an Huef, Laca, Raeburn, and Sims. We make an explicit construction of all KMS beta states for beta above a critical inverse temperature beta(c), as well as a precise description of the KMS states for graphs with a certain strongly connected subgraph. In addition, we find a correspondence between the KMS states of a graph algebra and its dual-graph algebra when E is a row-finite graph with no sinks.