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

2016/09/09 by Lisa Orloff Clark, Clark, Lisa Orloff, Ruy Exel +3 · 1 citation
Mathematics · #Advanced Topology and Set Theory #Mathematical and Theoretical Analysis #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1609.02873

Abstract

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

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• Nonunital prime rings graded by ordered groups

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