KMS and ground states on ultragraph \( C^*\)-algebras (Q1990920)

Using the partial crossed product description of ultragraph \(C^*\)-algebras, the authors show that the KMS states associated with \(C^*(\mathcal{G})\) -- with \(\mathcal{G}\) an ultragraph having no sinks and satisfying a certain condition (RFUM) -- can be identified with a subset of the state space of the abelian \(C^*\)-algebra of continuous functions on the shift space associated with \(\mathcal{G}\). The ground states associated to \(C^*(\mathcal{G})\) are also characterized.