A noncommutative generalization of stone duality

M. V. Lawson

doi:10.1017/S1446788710000145

A noncommutative generalization of stone duality

M. V. Lawson

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

Abstract

We prove that the category of boolean inverse monoids is dually equivalent to the category of boolean groupoids. This generalizes the classical Stone duality between boolean algebras and boolean spaces. As an instance of this duality, we show that the boolean inverse monoid C_n associated with the Cuntz groupoid G_n is the strong orthogonal completion of the polycyclic (or Cuntz) monoid P_n. The group of units of C_n is the Thompson group V_n,1. Copyright © Australian Mathematical Publishing Association Inc. 2010.

Original language	English
Pages (from-to)	385-404
Number of pages	20
Journal	Journal of the Australian Mathematical Society
Volume	88
Issue number	3
DOIs	https://doi.org/10.1017/S1446788710000145
Publication status	Published - Jun 2010

Keywords

étale topological groupoid
inverse semigroup
stone duality

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10.1017/S1446788710000145

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abstract = "We prove that the category of boolean inverse monoids is dually equivalent to the category of boolean groupoids. This generalizes the classical Stone duality between boolean algebras and boolean spaces. As an instance of this duality, we show that the boolean inverse monoid Cn associated with the Cuntz groupoid Gn is the strong orthogonal completion of the polycyclic (or Cuntz) monoid Pn. The group of units of Cn is the Thompson group Vn,1. Copyright {\textcopyright} Australian Mathematical Publishing Association Inc. 2010.",

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AB - We prove that the category of boolean inverse monoids is dually equivalent to the category of boolean groupoids. This generalizes the classical Stone duality between boolean algebras and boolean spaces. As an instance of this duality, we show that the boolean inverse monoid Cn associated with the Cuntz groupoid Gn is the strong orthogonal completion of the polycyclic (or Cuntz) monoid Pn. The group of units of Cn is the Thompson group Vn,1. Copyright © Australian Mathematical Publishing Association Inc. 2010.

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KW - inverse semigroup

KW - stone duality

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JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

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ER -

A noncommutative generalization of stone duality

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Keywords

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