Analysis and Probability Seminar

Given a left cancellative monoid, there is a natural definition of its reduced C*-algebra arising from the left regular representation. It is much less clear how to define a full C*-algebra. The problem has over the years attracted attention of a number of mathematicians and by now has been solved for a relatively large class of monoids. One of the approaches is to construct groupoid models for the reduced C*-algebras. The question when such models actually work is part of the more general question of how to determine a faithful family of representations of a reduced groupoid C*-algebra. I'll explain a partial solution of the latter problem and discuss its application to semigroup C*-algebras. (Joint work with Gaute Schwartz.)