Matteo Pagliero, KU Leuven
"Classification of equivariantly \mathcal{O}2-stable amenable actions on nuclear C*-algebras"
The classification of group actions on C*-algebras is an active research theme in the field of Operator Algebras. Although there has recently been substantial progress in the classification of group actions on simple, separable, nuclear, purely infinite C*-algebras, the non-simple case is not yet fully explored in the literature. In this talk, I will present joint work with G. Szabó, in which we classify well-behaved locally compact group actions on separable, nuclear C*-algebras that are not necessarily simple and tensorially absorb the Cuntz algebra \mathcal{O}2. Our main result states that an amenable, isometrically shift-absorbing, equivariantly \mathcal{O}2-stable action on a separable, nuclear, stable (or unital) C*-algebra is classified up to cocycle conjugacy by a topological dynamical system on the space of primitive ideals of the C*-algebra. This may be considered as a dynamical generalisation of Gabe--Kirchberg's \mathcal{O}2-stable classification theorem. In the first part of the talk, I will introduce the aforementioned assumptions, and provide a full description of the classification invariant. In the second part, I will give an overview of our classification theorem, and elaborate on how it relates to the existing literature.
This seminar will be held both online and in person:
- Room: MC 5479
- Zoom link: https://uwaterloo.zoom.us/j/94186354814?pwd=NGpLM3B4eWNZckd1aTROcmRreW96QT09