Probabilistic Operator Algebra seminar: Fixed-point properties for actions on cones and invariant traces on C*-algebras
Seminar | April 27 | 9-10:30 a.m. | 736 Evans Hall
Mikael Rordam, University of Copenhagen
Nicolas Monod has in a recent paper introduced a new class of groups with the fixed-point property for cones, characterized by always admitting a non-trivial fixed-point whenever they act on cones (under some additional hypothesis). He showed that this class contains all groups of sub-exponential growth and is contained in the class of supramenable groups. (It is not known if these three classes are distinct). He proved a number of equivalent conditions to be a group with the fixed-point property for cones, and he established a list of permanence properties for this class of groups. Monod's results have applications for the existence of invariant traces on a (non-unital) C*-algebra equipped with an action of a group. The purpose of the talk will be to explain some of Monod's results and their applications to C*-algebras. As an example we describe traces on the Roe algebra.