The tight groupoid of an inverse semigroup

By R. Exel, Enrique Pardo. Semigroup Forum, 2014

68 citations recorded by the source corpus.

In this work we present algebraic conditions on an inverse semigroup S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document} (with zero) which imply that its associated tight groupoid Gtight(S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}_\mathrm{tight}(\mathcal {S})$$\end{document} is: Hausdorff, essentially principal, minimal and contracting, respectively. In some cases these conditions are in fact necessary and sufficient.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b28cf40480c3ab15da9efd26c7473ec096740258

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Ben Steinberg
2. Enrique Pardo
3. R. Exel
4. Aidan Sims
5. L. O. Clark
6. Charles Starling
7. Mark V. Lawson
8. Mikhailo Dokuchaev

In Mathematical Physics

1. Ben Steinberg
2. Enrique Pardo
3. Aidan Sims
4. L. O. Clark
5. R. Exel
6. Charles Starling
7. Mark V. Lawson
8. P. Ara

Citations in the corpus

• Self-similar graphs, a unified treatment of Katsura and Nekrashevych C*-algebras (2014, methodology): “It is worth noticing that many results of [13] used in the above proof, such as [13: Proposition 6.”
• Simplicity, primitivity and semiprimitivity of etale groupoid algebras with applications to inverse semigroup algebras (2014, background): “We then discuss inverse semigroup algebras and discuss how topological properties of groupoids of germs relate to dynamical properties of inverse semigroup actions (see the historical discussion below for connections with [10]).”
• Simplicity of algebras associated to non-Hausdorff groupoids (2018, background): “For any unreferenced claims in this section, see [11] and [12].”