Ideals of Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras

TL;DR

This paper characterizes the ideal structure of Steinberg algebras associated with strongly effective Hausdorff groupoids over any commutative ring, providing new insights even for Leavitt path algebras.

Contribution

It offers a complete description of the ideal lattice for Steinberg algebras of strongly effective groupoids, extending known results to a broader class.

Findings

Complete ideal lattice description for strongly effective groupoid Steinberg algebras

New results applicable to Leavitt path algebras

Explicit examples illustrating the theory

Abstract

We consider the ideal structure of Steinberg algebras over a commutative ring with identity. We focus on Hausdorff groupoids that are strongly effective in the sense that their reductions to closed subspaces of their unit spaces are all effective. For such a groupoid, we completely describe the ideal lattice of the associated Steinberg algebra over any commutative ring with identity. Our results are new even for the special case of Leavitt path algebras; so we describe explicitly what they say in this context, and give two concrete examples.