Proper actions, fixed-point algebras, and deformation via coactions

Abstract: The notion of proper actions of groups on spaces has various generalizations for group actions of noncommutative $C^*$-algebras $A$, which all allow the construction of generalized fixed-point algebras $A^G$ which are Morita equivalent to ideals in the reduced crossed products $A\rtimes_rG$. The weakest version was introduced by Rieffel in 1990 and it played an important role in his theory of deformations via actions of $\mathbb R^d$. In this talk we want to report on some joint work with Alcides Buss on a version of proper actions which allows the construction of maximal (or exotic) generalized fixed-point algebras which are Morita equivalent to ideals in the maximal (resp. exotic) crossed products. We will report on several applications including Landstad duality for coactions and deformation of C*-algebras via coactions in the sense of Kasprzak and Bowmick, Neshveyev, and Sangha.

operator algebras

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

The zoom links will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.