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

Clark, Lisa; Edie-Michell, Cain; an Huef, Astrid; Sims, Aidan

doi:10.1090/tran/7460

Ideals of Steinberg algebras of strongly effective groupoids, with applications to Leavitt path algebras
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by Lisa Orloff Clark, Cain Edie-Michell, Astrid an Huef and Aidan Sims PDF

Trans. Amer. Math. Soc. 371 (2019), 5461-5486 Request permission

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.

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