Dynamics, Geometry and C*-algebras

Speaker: : Elias Katsoulis (East Carolina)

Title: Hyperrigidity for operator algebras

Abstract: A non-selfadjoint operator algebra A is said to be hyperrigid if every non-degenerate ∗-representation of its C*-envelope has the property that it is the only completely contractive and completely positive extension of its restriction to A. The concept of hyperrigidity was first studied systematically by Arveson. In this talk we provide a detailed introduction to hyperrigidity and we exhibit many algebras which satisfy this property. Furthermore,  we explain how hyperrigidity relates to several open problems, including crossed product formulas for non-selfadjoint operator algebras and the Hao-Ng isomorphism in C*-algebras.