Some quasi-isometric invariants for inverse semigroups

Abstract: Coarse geometry is the study of metric spaces from a point of view far away, that is, up to coarse equivalence. Possibly the most studied factory of examples are finitely generated groups, which are naturally equipped with the path length metric of their Cayley graphs. One can then move onto the context of inverse semigroups where, for various reasons we will detail, one has to study its Schützenberger graphs. Properties of the semigroup that are invariant under coarse equivalence, such as the growth type and the number of ends, are here of particular interest.

In this talk we will be interested in two other properties, namely amenability and property A. Amenability was introduced by Day in 1957 as the existence of an invariant measure of the semigroup, but it can be characterized from a geometric point of view in the Schützenberger graphs of the semigroup. Viewed from this point of view, we will derive a certain necessary condition and prove that it's a quasi-isometric invariant. Much more recent is property A. In the talk we will define it and discuss its uses and possible characterizations, mostly in relation with C*-algebras.

This is based on joint work with Fernando Lledó and Pere Ara.

functional analysisgroup theoryrings and algebras

Audience: researchers in the topic

York semigroup seminar

Series comments: Description: Semigroup-related research talks at University of York.

Email Nora Szakacs at nora.szakacs@york.ac.uk for the meeting password.