ΕΚΔΗΛΩΣΕΙΣ

Ημερομηνία: Παρασκευή, 17 Φεβρουαρίου 2023
Ώρα: 17:00
Τόπος: Αίθουσα Γ31
Oμιλητής: S. Raum (Stockholm, Sw)
Τίτλος: Detecting ideals in reduced crossed product C*-algebras of topological dynamical systems
Περίληψη: Crossed products arising from topological dynamical systems are an important source of examples of C*-algebras and form ground for interaction between dynamics and operator algebras. Included in this class are reduced group C*-algebras which code representation theoretic information of a group. Sophisticated tools to prove (non-)simplicity of such C*-algebras have been developed over the time. However, they only apply to well-behaved dynamical systems or exclude a certain kind of amenable behaviour of the dynamical system. I will make these statements precise and report on joint work with Are Austad (University of Southern Denmark) in which we introduce the ℓ¹-ideal intersection property. All non-zero ideals in the crossed product C*-algebra of a dynamical system satisfying this property can be detected already inside the much smaller and more concrete ℓ¹-crossed product. We prove that large classes of groups, such as lattices in Lie groups and linear groups over algebraic integers in a number field have this property for ANY action on a locally compact Hausdorff space. The proof combines the theory of twisted groupoid C*-algebras and C*-simplicity with structure results about amenable subgroups.

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