On conjugacies of $C^*$-dynamical systems

Wei Sun

8:30 am to 9:20 am, June 3rd, 2015   Science Building A1414

Abstract:

Crossed product $C^*$-algebras contains information on both the original base $C^*$-algebras and the group actions. We focus on such problems as how we can derive certain conjugacies of two actions from the information of the two crossed product $C^*$-algebras.

We will start with reviewing some classical cases and results, and we will show some theoretical limits of those results. In particular, we will demonstrate examples of non-conjugacies in case the two crossed products are isomorphic. Based on that, we will show how the strengthened isomorphisms (approximate $K$-conjugacies as for those examples) can ensure the existence of such conjugacies for the above mentioned examples.