Ideals of Steinberg Algebras of Strongly Effective Groupoids, with Applications to Leavitt Path Algebras

Authors

Lisa Orloff Clark, University of Otago
Cain Edie-Mitchell, Australian National University
Astrid An Huef, University of OtagoFollow
Aidan Sims, University of WollongongFollow

RIS ID

134937

Publication Details

Clark, L., Edie-Mitchell, C., an Huef, A. & Sims, A. (2019). Ideals of Steinberg Algebras of Strongly Effective Groupoids, with Applications to Leavitt Path Algebras. Transactions Of The American Mathematical Society, 371 (8), 5461-5486.

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.

Grant Number

ARC/DP150101598