The lattice of ideals in the Steinberg algebra of a strongly effective groupoid

Abstract

A topological groupoid is generalization of topological group where the binary operation is only partially defined. Ample groupoids are a special class of topological groupoid that have an especially well behaved topology. To each ample groupoid G and commutative ring R (with 1), we consider the Steinberg R-algebra of G, which has become an important object of study in both ring theory and functional analysis. In this talk, I will present results about the ideal structure of a certain class of Steinberg algebras. In particular, we will take a close look at the lattice of ideals and an innovative approach to studying the join and meet operations.