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arXiv · 1609.02873

A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras

Lisa Orloff Clark·Ruy Exel·Enrique Pardo
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Abstract

Given an ample, Hausdorff groupoid $\mathcal{G}$, and a unital commutative ring $R$, we consider the Steinberg algebra $A_R(\mathcal {G})$. First we prove a uniqueness theorem for this algebra and then, when $\mathcal{G}$ is graded by a cocycle, we study graded ideals in $A_R(\mathcal {G})$. Applications are given for two classes of ample groupoids, namely those coming from actions of groups on graphs, and also to groupoids defined in terms of Boolean dynamical systems.

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Lisa Orloff Clark, Ruy Exel, Enrique Pardo. 2016-09-09. A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras. https://arxiv.org/abs/1609.02873

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