Professor Mikael Rørdam (University of Copenhagen): Group actions on compact
Thursday, 05.04.2012 16:30 im Raum M5
"Group actions on compact and locally compact spaces and their C-algebras"
Kirchberg and Phillips proved in the mid 1990s that the socalled Kirchberg
C-algebras are classified by K-theory. In a joint work with Sierakowski
we proved that every exact and non-amenable countable discrete
group admits a free minimal amenable action on the Cantor set X such
that C(X) ored is a Kirchberg algebra. The proof relies on properties
of the Roe algebra `1() o and Tarskis characterization of paradoxical
sets in a group. For the similar result for actions on a non-compact locally
compact Hausdorff space one needs to consider the so-called supramenable
groups, which are groups that contain no paradoxical subset. We
show that every (exact) non-supramenable group admits a free minimal
amenable action on the locally compact non-compact Cantor set such that
the crossed product is a (non-unital) Kirchberg algebra. This is a part of an
ongoing joint work with Kellerhals and Monod.