Larissa Kroell, University of Waterloo
Analysis Seminar: Injective Envelopes for partial C*-dynamical systems
Given a C*-dynamical system, a fruitful avenue to study its properties has been to study the dynamics on its injective envelope. This approach relies on the result of Kalantar and Kennedy (2017), who show that C*-simplicity can be characterized via the Furstenberg boundary using injective envelope techniques. Inspired by this use case, we generalize the notion of injective envelope to partial C*-dynamical systems. Partial group actions are a generalization of group actions and first introduced for C*-algebras by Ruy Exel (1994) to express certain C*-algebras as crossed products by a single partial automorphism. In this talk, we give a short introduction to partial actions and show the existence of an injective envelope for unital partial C*-dynamical systems. Additionally, we discuss its connection to enveloping actions. This is based on joint work with Matthew Kennedy and Camila Sehnem.
MC 5417