Filtering germs: Groupoids associated to inverse semigroups

Becky Armstrong; Lisa Orloff Clark; Astrid an Huef; Malcolm Jones; Ying-Fen Lin

doi:10.1016/j.exmath.2021.07.001

Filtering germs: Groupoids associated to inverse semigroups

Becky Armstrong^*, Lisa Orloff Clark, Astrid an Huef, Malcolm Jones, Ying-Fen Lin

^*Corresponding author for this work

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Abstract

We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.

Original language	English
Pages (from-to)	127-139
Number of pages	13
Journal	Expositiones Mathematicae
Volume	40
Issue number	1
Early online date	15 Jul 2021
DOIs	https://doi.org/10.1016/j.exmath.2021.07.001
Publication status	Published - 01 Mar 2022

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Filtering germs: Groupoids associated to inverse semigroups
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title = "Filtering germs: Groupoids associated to inverse semigroups",

abstract = "We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.",

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AU - Armstrong, Becky

AU - Clark, Lisa Orloff

AU - an Huef, Astrid

AU - Jones, Malcolm

AU - Lin, Ying-Fen

PY - 2022/3/1

Y1 - 2022/3/1

N2 - We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.

AB - We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.

U2 - 10.1016/j.exmath.2021.07.001

DO - 10.1016/j.exmath.2021.07.001

M3 - Article

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VL - 40

SP - 127

EP - 139

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 1

ER -

Filtering germs: Groupoids associated to inverse semigroups

Abstract

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