# Convolution semigroups on quantum groups and non-commutative Dirichlet forms

Seminar
Speaker
Dr. Ami Viselter University of Haifa
Date
06/11/2017 - 15:20 - 14:00Add to Calendar 2017-11-06 14:00:00 2017-11-06 15:20:00 Convolution semigroups on quantum groups and non-commutative Dirichlet forms We will discuss convolution semigroups of states on locally compact quantum groups. They generalize the families of distributions of Levy processes from probability. We are particularly interested in semigroups that are symmetric in a suitable sense. These are proved to be in one-to-one correspondence with KMS-symmetric Markov semigroups on the $L^{\infty}$ algebra that satisfy a natural commutation condition, as well as with non-commutative Dirichlet forms on the $L^2$ space that satisfy a natural translation invariance condition. This Dirichlet forms machinery turns out to be a powerful tool for analyzing convolution semigroups as well as proving their existence. We will use it to derive geometric characterizations of the Haagerup Property and of Property (T) for locally compact quantum groups, unifying and extending earlier partial results. We will also show how examples of convolution semigroups can be obtained via a cocycle twisting procedure. Based on joint work with Adam Skalski. 2nd floor Colloquium Room, Building 216 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
2nd floor Colloquium Room, Building 216
Abstract

We will discuss convolution semigroups of states on locally
compact quantum groups. They generalize the families of distributions
of Levy processes from probability. We are particularly interested
in semigroups that are symmetric in a suitable sense. These are proved
to be in one-to-one correspondence with KMS-symmetric Markov semigroups
on the $L^{\infty}$ algebra that satisfy a natural commutation condition,
as well as with non-commutative Dirichlet forms on the $L^2$ space
that satisfy a natural translation invariance condition. This Dirichlet
forms machinery turns out to be a powerful tool for analyzing convolution
semigroups as well as proving their existence. We will use it to derive
geometric characterizations of the Haagerup Property and of Property (T)
for locally compact quantum groups, unifying and extending earlier
partial results. We will also show how examples of convolution semigroups
can be obtained via a cocycle twisting procedure. Based on joint work