Journal ArticleDOI
The Polycyclic Monoids P n and the Thompson Groups V n,1
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The strong orthogonal completion of the polycyclic monoid P n on n generators was constructed in this paper, where the group of units is the Thompson group of generators.Abstract:
We construct what we call the strong orthogonal completion C n of the polycyclic monoid P n on n generators. The inverse monoid C n is congruence free and its group of units is the Thompson group V...read more
Citations
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Non-commutative stone duality: inverse semigroups, topological groupoids and c*-algebras
TL;DR: In this paper, a non-commutative generalization of Stone duality that connects a class of inverse semigroups called Boolean inverse ∧-semigroups, called Hausdorff Boolean groupoids, with topological groupoids was studied.
Journal ArticleDOI
Pseudogroups and their étale groupoids
Mark V. Lawson,Daniel Lenz +1 more
TL;DR: The theory of pseudogroups motivated by applications to group theory, such as C ∗ -algebras and aperiodic tilings, has been studied in this article.
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A noncommutative generalization of stone duality
TL;DR: In this article, it was shown that the category of boolean inverse monoids is dually equivalent to the class of boolean groupoids, which generalizes the classical Stone duality between boolean algebras and boolean spaces.
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Pseudogroups and their etale groupoids
Mark V. Lawson,Daniel Lenz +1 more
TL;DR: The theory of pseudogroups motivated by applications to group theory, such as C*-algebras and aperiodic tilings, has been studied in this paper.
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Graph inverse semigroups: their characterization and completion
David G. Jones,Mark V. Lawson +1 more
TL;DR: In this article, the Cuntz-Krieger semigroup of the graph was shown to be the ample semigroup for a topological groupoid associated with the graph.
References
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Book
Automata, Languages, and Machines
TL;DR: This book attempts to provide a comprehensive textbook for undergraduate and postgraduate mathematicians with an interest in formal languages and automata, written by Professor Ian Chiswell.
Book
Inverse Semigroups, the Theory of Partial Symmetries
TL;DR: Inverse semigroups as mentioned in this paper, Ehresmann's maximum enlargement theorem complements the type II theorem of inverse monoids and formal languages for inverse monoid inverse semiggroups.
Book
Groupoids, Inverse Semigroups, and their Operator Algebras
TL;DR: Inverse semigroups and locally compact groupoids have been studied in the context of representation theory for groupoids that are r-discrete and their inverse groups of open G-sets.