Groupoids and Steinberg Algebras

Abstract

A groupoid is a generalisation of group in which composition is only partially defined. In first half of this talk, I will give an overview of groupoid theory and show how groupoids provide a unifying model for a number of seemingly unrelated mathematical structures.

In the second half of the talk, I will give an overview of the theory of Steinberg algebras. A Steinberg algebra is constructed from an `ample' topological groupoid. Once again, these algebras can be used to model a number of seemingly unrelated algebraic constructions.