An algebraic approach to the Weyl groupoid

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 s...

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Bibliographic Details
Published in:Journal of algebra 2021-02, Vol.568, p.193-240
Main Author: Bice, Tristan
Format: Article
Language:English
Subjects:
C-algebra
Inverse semigroup
ring
semigroup
Tight groupoid
Weyl groupoid
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.10.010