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A NONCOMMUTATIVE GENERALIZATION OF STONE DUALITY

Part of: Semigroups

Published online by Cambridge University Press:  05 May 2010

M. V. Lawson
M. V. Lawson*
Affiliation:
Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, Scotland (email: [email protected])
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Abstract

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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.

Keywords

inverse semigroupétale topological groupoidstone duality

MSC classification

Secondary: 20M18: Inverse semigroups 06E15: Stone spaces (Boolean spaces) and related structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 3 , June 2010 , pp. 385 - 404
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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