The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations

DOI10.4171/JNCG/400zbMath1481.46052arXiv1902.02583OpenAlexW2999952163MaRDI QIDQ2043510

Mark V. Lawson, Alina Vdovina

Publication date: 2 August 2021

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.02583

zbMATH Keywords

Stone dualityinverse semigroupsCuntz-Krieger relationsample groupoids

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Topological groupoids (including differentiable and Lie groupoids) (22A22) Inverse semigroups (20M18)

Related Items (8)

The type semigroup, comparison, and almost finiteness for ample groupoids ⋮ Higher dimensional generalizations of the Thompson groups ⋮ Zappa-Szép products for partial actions of groupoids on left cancellative small categories ⋮ Non-commutative Stone duality ⋮ Tight and cover-to-join representations of semilattices and inverse semigroups ⋮ An algebraic characterisation of ample type I groupoids ⋮ Quotients of the Booleanization of an Inverse Semigroup ⋮ The Polycyclic Inverse Monoids and the Thompson Groups Revisited

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• AF inverse monoids and the structure of countable MV-algebras
• Graph inverse semigroups: their characterization and completion.
• The tiling \(C^*\)-algebra viewed as a tight inverse semigroup algebra
• Higher-rank graph \(C^*\)-algebras: an inverse semigroup and groupoid approach
• Étale groupoids and their quantales
• Simplicity, primitivity and semiprimitivity of étale groupoid algebras with applications to inverse semigroup algebras
• Inverse semigroups and combinatorial \(C^*\)-algebras
• A groupoid approach to discrete inverse semigroup algebras
• On localizations and simple \(C^*\)-algebras
• A groupoid approach to C*-algebras
• A class of C*-algebras and topological Markov chains
• Simple \(C^*\)-algebras generated by isometries
• Groupoids, inverse semigroups, and their operator algebras
• The local structure of tilings and their integer group of coinvariants
• The \(C^*\)-algebras of finitely aligned higher-rank graphs
• Higher rank graph \(C^*\)-algebras
• Tiling semigroups
• Refinement monoids, equidecomposability types, and Boolean inverse semigroups
• The Booleanization of an inverse semigroup
• On strong affine representations of the polycyclic monoids
• Strong representations of the polycyclic inverse monoids: cycles and atoms.
• Pseudogroups and their étale groupoids.
• THE ÉTALE GROUPOID OF AN INVERSE SEMIGROUP AS A GROUPOID OF FILTERS
• Groupoids and $C^*$-algebras for categories of paths
• Groupoids and C*-algebras for left cancellative small categories
• Orthogonal Completions of the Polycyclic Monoids
• ON AN ORDER-BASED CONSTRUCTION OF A TOPOLOGICAL GROUPOID FROM AN INVERSE SEMIGROUP
• A NONCOMMUTATIVE GENERALIZATION OF STONE DUALITY
• Iterated function systems and permutation representations of the Cuntz algebra
• Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras
• Topological equivalence of tilings
• NON-COMMUTATIVE STONE DUALITY: INVERSE SEMIGROUPS, TOPOLOGICAL GROUPOIDS AND C*-ALGEBRAS
• THE GROUPS OF RICHARD THOMPSON AND COMPLEXITY
• The Polycyclic MonoidsP_nand the Thompson GroupsV_n,1
• JOINS AND COVERS IN INVERSE SEMIGROUPS AND TIGHT -ALGEBRAS
• The Theory of Representation for Boolean Algebras
• Applications of the Theory of Boolean Rings to General Topology
• Compactable semilattices

This page was built for publication: The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations