The tight groupoid of an inverse semigroup

2014/08/22 by Exel, Ruy, Pardo, Enrique · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1408.5278

Abstract

In this work we present algebraic conditions on an inverse semigroup S (with zero) which imply that its associated tight groupoid G_tight)(S) is: Hausdorff, essentially principal, minimal and contracting, respectively. In some cases these conditions are in fact necessary and sufficient.

Cited by

• Minimality and effectiveness of the groupoid associated to a self-similar ultragraph
• The action of an inverse semigroup on its Stone-Čech compactification

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• The tight groupoid of the inverse semigroups of left cancellative small categories
• The action of an inverse semigroup on its Stone-Čech compactification
• Condition (K) for inverse semigroups and the ideal structure of their C^*-algebras
• Consonant inverse semigroups
• Inverse Semigroups and Combinatorial C*-Algebras