A NONCOMMUTATIVE GENERALIZATION OF STONE DUALITY

By Mark V. Lawson. Journal of the Australian Mathematical Society, 2009

71 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/791632bb574e93cb6ab0cb666970f3d6bc8e3fef

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Citations in the corpus

Pseudogroups and their étale groupoids (2011, background): “y assumption d(ai) ∈ E(A) for some i. Now a,d(ai) ∈ A and A is an inverse subsemigroup and so ai = ad(ai) ∈ A, as required. The proof of our claim concerning ultraﬁlters follows from Proposition 2.13 [12] since the argument used there in fact works in any inverse semigroup. Our ﬁrst important result”
Graph inverse semigroups: their characterization and completion (2011, background): “d associated with the graph, and the semigroup analogue of the Leavitt path algebra of the graph. 1. Introduction This paper is part of an ongoing programme to develop non-commutative Stone dualities [29, 30, 31, 32] linking inverse semigroups, topological groupoids and C∗- algebras. Our goal here i”