# 28 novembre 2017: 1 événement

### Mardi 28 novembre 2017 13:45-15:00 - Adam Skalski - IMPAN, Varsovie

Translation invariant Dirichlet forms in the context of locally compact quantum groups

Résumé : Since the work of Cipriani on one hand and Goldstein and Lindsay on the other in the 1990s it is known that certain natural class of symmetric Markov semigroups on a von Neumann algebra M equipped with a faithful normal state admits
extensions to associated Haagerup $L^p$-spaces and is characterised via a Dirichlet property of the generating quadratic form on the
$L^2$-space.
Recently Cipriani, Franz and Kula studied a special class of such semigroups associated to compact quantum groups. In this talk I will discuss how their results extend to the framework of locally compact quantum groups, where two new important technical features appear : there is no natural `algebraic’ domain for the generator and one needs to work with weights, as opposed to finite states (using the appropriate Dirichlet form result provided by Goldstein and Lindsay). I will also present some applications of Dirichlet forms to the study of geometric properties of quantum groups.
This is based on the joint work with A.Viselter.

En savoir plus : Séminaire d’Analyse Fonctionnelle