Groups and Operator Algebras Seminar

Speaker: Matteo Pagliero (Southern Denmark University)

Title:  Corona algebras and strongly self-absorbing C*-dynamics

Abstract:  Recent work of Farah and of Farah-Szabó established a powerful link between absorption properties of non-unital C*-algebras and their corona algebras (i.e. quotients of the multiplier algebra by the algebra itself). They showed that if a non-unital C*-algebra tensorially absorbs a strongly self-absorbing C*-algebra, then every relative commutant (by a separable subalgebra) in its corona must contain a unital copy of that strongly self-absorbing algebra. In this talk, I will present a dynamical analogue of this result, establishing a new connection between absorption phenomena and the structure of corona actions. As an intermediate step toward the main theorem, I will show that corona actions enjoy what we call the dynamical folding property. This is a strong structural feature that generalises an earlier insight of Phillips and Weaver. All results discussed are based on joint work with Xiuyuan Li and Gábor Szabó, avilable on arXiv.