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Fixed-point results for cones and invariant traces on C*-algebras

Banff International Research Station for Mathematical Innovation and Discovery

Nicolas Monod has in a recent paper introduced a new class of groups, groups with 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 relevance for the existence of invariant traces on a (non-unital) C*-algebra with an action of a group. The purpose of my talk will be to explain some of Monod’s results and some of their applications to C*-algebras.

Mathematics; Functional analysis; Operator theory

video/mp4

Author affiliation: University of Copenhagen

2018-04-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/65078

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/