# Étale Groupoids and Steinberg Algebras a Concise Introduction

@article{Clark2020taleGA, title={{\'E}tale Groupoids and Steinberg Algebras a Concise Introduction}, author={Lisa Orloff Clark and Roozbeh Hazrat}, journal={arXiv: Rings and Algebras}, year={2020}, pages={73-101} }

We give a concise introduction to (discrete) algebras arising from etale groupoids (aka Steinberg algebras) and describe their close relationship with groupoid \(C^*\)-algebras. Their connection to partial group rings via inverse semigroups is also explored.

#### 5 Citations

The Groupoids of Adaptable Separated Graphs and Their Type Semigroups

- Mathematics
- 2019

Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup,… Expand

A note on the core of Steinberg algebras.

- Mathematics
- 2019

In this short note we show that, for an ample Hausdorff groupoid $G$, and the Steinberg algebra $A_R(G)$ with coefficients in the commutative ring $R$, the centraliser of subalgebra $A_R(G^{(0)})$ of… Expand

The talented monoid of a directed graph with applications to graph algebras

- Mathematics
- 2020

It is a conjecture that for the class of Leavitt path algebras associated to finite directed graphs, their graded Grothendieck groups $K_0^{\mathrm{gr}}$ are a complete invariant. For a Leavitt path… Expand

A classification of ideals in Steinberg and Leavitt path algebras over arbitrary rings

- Mathematics
- Journal of Algebra
- 2021

We give a one-to-one correspondence between ideals in the Steinberg algebra of a Hausdorff ample groupoid G, and certain families of ideals in the group algebras of isotropy groups in G. This… Expand

Graded Semigroups.

- Mathematics
- 2020

We systematically develop a theory of graded semigroups, that is semigroups S partitioned by groups G, in a manner compatible with the multiplication on S. We define a smash product S#G, and show… Expand

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