AG Lie-Gruppen: J. Christensen (KU Lueven): (Non)exotic completions of the group algebras of isotropy groups

Vortragender: Johannes Christensen, KU Leuven
Einladender: Kang Li

Abstract:
The so-called groupoid C*-algebras play an important role in the theory of
C*-algebras, since there are an abundance of examples of C*-algebras that can
be
described concretely as such groupoid C*-algebras. To any locally compact
étale
groupoid one can associate two C*-algebras, namely the full groupoid
C*-algebra
and the reduced groupoid C*-algebra. There exists a useful description of a
large class of important states on the full groupoid C*-algebra. In this talk
I
will report on a joint project with Sergey Neshveyev where we study which of
these states that factors through the reduced groupoid C*-algebra.

I will introduce a new C*-norm on the group algebras of the isotropy groups of
a
locally compact étale groupoid, and argue that this norm completely
characterizes when the states we consider factors through the reduced groupoid
C*-algebra. I will then present examples which illustrate that our C*-norm can
coincide with the full norm, that it can be a genuine exotic norm, but that it
in many standard examples always is the reduced norm.