On KMS weights of C*-algebras associated to topological graphs

Abstract

In this thesis we give a complete description of the extremal $\beta$-KMS weights for the gauge-action on the $C^*$-algebra associated to a second-countable topological graph. We give a description in terms of ergodic measures $\nu$ on the boundary path space $\partial E$ satisfying $\sigma^*\nu = e^\beta\nu$ on $\partial E \setminus E^0$. And a description in terms of extremal $\beta$-sub-invariant measures $\mu$ on the vertex space $E^0$. We also develop some theory about regular Borel measure using sheaf-theory that has been useful for comparing different measures and gives a new description of the pullback of a regular Borel measure along a local homeomorphism.

In this thesis we give a complete description of the extremal $\beta$-KMS weights for the gauge-action on the $C^*$-algebra associated to a second-countable topological graph. We give a description in terms of ergodic measures $\nu$ on the boundary path space $\partial E$ satisfying $\sigma^*\nu = e^\beta\nu$ on $\partial E \setminus E^0$. And a description in terms of extremal $\beta$-sub-invariant measures $\mu$ on the vertex space $E^0$. We also develop some theory about regular Borel measure using sheaf-theory that has been useful for comparing different measures and gives a new description of the pullback of a regular Borel measure along a local homeomorphism.