The tight groupoid of the inverse semigroups of left cancellative small categories

2019/06/18 by Ortega, Eduard, Pardo, Enrique · 1 citation
#20L05 #46L05 #46L55 #46L80 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1906.07487

Abstract

We fix a path model for the space of filters of the inverse semigroup S_Λ associated to a left cancellative small category Λ. Then, we compute its tight groupoid, thus giving a representation of its C^*-algebra as a (full) groupoid algebra. Using it, we characterize when these algebras are simple. Also, we determine amenability of the tight groupoid under mild, reasonable hypotheses.

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Related

• Inverse Semigroups and Combinatorial C*-Algebras
• The tight groupoid of an inverse semigroup
• Groupoids and C^*-algebras for left cancellative small categories
• Condition (K) for inverse semigroups and the ideal structure of their C^*-algebras
• The etale groupoid of an inverse semigroup as a groupoid of filters