# Equivalent groupoids have Morita equivalent Steinberg algebras

@article{Clark2013EquivalentGH, title={Equivalent groupoids have Morita equivalent Steinberg algebras}, author={Lisa Orloff Clark and Aidan Sims}, journal={Journal of Pure and Applied Algebra}, year={2013}, volume={219}, pages={2062-2075} }

## 67 Citations

### Simple flat Leavitt path algebras are von Neumann regular

- MathematicsCommunications in Algebra
- 2019

Abstract For a unital ring, it is an open question whether flatness of simple modules implies all modules are flat and thus the ring is von Neumann regular. The question was raised by Ramamurthi over…

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

- MathematicsTransactions of the American Mathematical Society
- 2018

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…

### Subsets of vertices give morita equivalences of Leavitt path algebras

- Mathematics
- 2017

We show that every subset of vertices of a directed graph E gives a Morita equivalence between a subalgebra and an ideal of the associated Leavitt path algebra. We use this observation to prove an…

### Reconstruction of graded groupoids from graded Steinberg algebras

- Mathematics
- 2016

We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over any commutative…

### Simplicity of algebras associated to non-Hausdorff groupoids

- MathematicsTransactions of the American Mathematical Society
- 2019

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…

### Prime étale groupoid algebras with applications to inverse semigroup and Leavitt path algebras

- MathematicsJournal of Pure and Applied Algebra
- 2019

### Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C*-algebras and Leavitt path algebras

- Mathematics
- 2016

We prove that ample groupoids with sigma-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of Kakutani…

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

- MathematicsIsrael Journal of Mathematics
- 2019

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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