Krzysztof Bardadyn

Simplicity of $L_p$-operator algebra crossed products

In 2010's Phillips initiated a program whose aim is to generalize large parts of the modern $C^*$-algebra theory to operator algebras acting on $L_p$-spaces. Since then a number of papers appeared establishing some strong results in this direction, but there are still some fundamental open problems. One of them, explicitly stated in Phillips (2013) and Gardella-Lupini (2017), is a characterization of simplicity of $L_p$-crossed products, and in particular a generalization of the $C^*$-algebraic results from the seminal paper of Archbold and Spielberg (1993).

In my talk I will present a solution to the aforementioned problem for an action of a discrete group on a locally compact Hausdorff space. The techniques work also for etale groupoids and give a characterization of the intersection property and simplicity of the correspodning $L_p$-operator algebras in terms of topological freeness.

Based on joint work with Bartosz Kwaśniewski and Andrew McKee.

XXXIX Workshop on Geometric Methods in Physics	19.06–25.06.2022
XI School on Geometry and Physics	27.06–1.07.2022

Event sponsored by:
University of Bialystok