An Algebraic Approach to the Weyl Groupoid

Abstract

We unify the Kumjian-Renault Weyl groupoid construction with the Lawson-Lenz version of Exel's tight groupoid construction. We do this by utilising only a weak algebraic fragment of the C*-algebra structure, namely its *-semigroup reduct. Fundamental properties like local compactness are also shown to remain valid in general classes of *-rings.

References in corpus (7)

• Etale groupoids and their quantales
• Reconstruction of groupoids and C*-rigidity of dynamical systems
• Étale groupoids and their $C^{\ast }$-algebras
• Noncommutative Cartan sub-algebras of C*-algebras
• General Non-Commutative Locally Compact Locally Hausdorff Stone Duality
• Quantales and Fell bundles
• Hausdorff Tight Groupoids Generalised

Cited by in corpus (2)

• Filtering germs: Groupoids associated to inverse semigroups
• Dauns-Hofmann-Kumjian-Renault Duality for Fell Bundles and Structured C*-Algebras