The tiling \(C^*\)-algebra viewed as a tight inverse semigroup algebra

DOI10.1007/s00233-011-9359-xzbMath1256.46034arXiv1106.4535OpenAlexW2065473952MaRDI QIDQ444647

Ruy Exel, Daniel Gonçalves, Charles Starling

Publication date: 16 August 2012

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.4535

zbMATH Keywords

\(C^*\)-algebratilinginverse semigrouptight representations

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05)

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The tight groupoid of an inverse semigroup ⋮ Inverse semigroups associated to subshifts ⋮ Inverse semigroups associated with one-dimensional generalized solenoids ⋮ Amenability and uniqueness for groupoids associated with inverse semigroups ⋮ \(C^\ast\)-algebras associated with Hilbert \(C^\ast\)-quad modules of finite type ⋮ Quantum phase transitions and localization in semigroup fredkin spin chain ⋮ Tight and cover-to-join representations of semilattices and inverse semigroups ⋮ Supersymmetric many-body systems from partial symmetries -- integrability, localization and scrambling ⋮ The universal Boolean inverse semigroup presented by the abstract Cuntz-Krieger relations ⋮ JOINS AND COVERS IN INVERSE SEMIGROUPS AND TIGHT -ALGEBRAS ⋮ Quotients of the Booleanization of an Inverse Semigroup ⋮ \(C^\ast\)-algebras associated with Hilbert \(C^\ast\)-quad modules of \(C^\ast\)-textile dynamical systems

Cites Work

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• Inverse semigroups and combinatorial \(C^*\)-algebras
• A groupoid approach to C*-algebras
• Space tilings and local isomorphism
• Nonperiodicity implies unique composition for self-similar translationally finite tilings
• The local structure of tilings and their integer group of coinvariants
• Pseudogroups and their étale groupoids.
• The l 1 -Algebra of a Commutative Semigroup
• C*-Algebras of inverse semigroups
• ON AN ORDER-BASED CONSTRUCTION OF A TOPOLOGICAL GROUPOID FROM AN INVERSE SEMIGROUP
• Representations of the l 1 -Algebra of an Inverse Semigroup
• Topological equivalence of tilings
• NONCOMMUTATIVE GEOMETRY OF TILINGS AND GAP LABELLING
• Inverse Semi-Groups