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Entropy and information causality in general probabilistic theories

In this addendum to our paper (2010 New J. Phys. 12 033024), we point out that an elementary consequence of the strong subadditivity inequality allows us to strengthen one of the main conclusions of…
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Simplicity of algebras associated to étale groupoids

We prove that the full C∗-algebra of a second-countable, Hausdorff, étale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G…
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Uniqueness Theorems for Steinberg Algebras

We prove Cuntz-Krieger and graded uniqueness theorems for Steinberg algebras. We also show that a Steinberg algebra is basically simple if and only if its associated groupoid is both effective and…
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Equivalent groupoids have Morita equivalent Steinberg algebras

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Simplicity of algebras associated to non-Hausdorff groupoids

We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a…
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A groupoid generalisation of Leavitt path algebras

Let $$G$$G be a locally compact, Hausdorff, étale groupoid whose unit space is totally disconnected. We show that the collection $$A(G)$$A(G) of locally-constant, compactly supported complex-valued…
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A Generalised uniqueness theorem and the graded ideal structure of Steinberg algebras

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

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…
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Using the Steinberg algebra model to determine the center of any Leavitt path algebra

Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient…
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Strongly graded groupoids and strongly graded Steinberg algebras

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