KMS states for the generalized gauge action on graph algebras

Abstract

Given a positive function on the set of edges of an arbitrary directed graph $E=(E^0,E^1)$, we define a one-parameter group of automorphisms on the C*-algebra of the graph $C^{\ast }(E)$, and study the problem of finding KMS states for this action. We prove that there are bijective correspondences between KMS states on $C^{\ast }(E)$, a certain class of states on its core, and a certain class of tracial states on $C_0(E^0)$. We also find the ground states for this action and give some examples.

Cited by in corpus (2)

• Partial actions and KMS states on relative graph $C^{\ast }$-algebras
• KMS and ground states on ultragraph C*-algebras