A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras
Abstract
Given an ample, Hausdorff groupoid G, and a unital commutative ring R, we consider the Steinberg algebra AR( G). First we prove a uniqueness theorem for this algebra and then, when G is graded by a cocycle, we study graded ideals in AR( 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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