Groupoid C*-algebras and ground states

24 September 2020
16:00
Nadia Larsen

Further Information: 

Part of UK virtual operator algebras seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home

Abstract

C*-algebras associated to etale groupoids appear as a versatile construction in many contexts. For instance, groupoid C*-algebras allow for implementation of natural one-parameter groups of automorphisms obtained from continuous cocycles. This provides a path to quantum statistical mechanical systems, where one studies equilibrium states and ground states. The early characterisations of ground states and equilibrium states for groupoid C*-algebras due to Renault have seen remarkable refinements. It is possible to characterise in great generality all ground states of etale groupoid C*-algebras in terms of a boundary groupoid of the cocycle (joint work with Laca and Neshveyev). The steps in the proof employ important constructions for groupoid C*-algebras due to Renault.

  • Functional Analysis Seminar