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

Ortega, Eduard; Pardo, Enrique

doi:10.1090/tran/8100

The tight groupoid of the inverse semigroups of left cancellative small categories
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by Eduard Ortega and Enrique Pardo PDF

Trans. Amer. Math. Soc. 373 (2020), 5199-5234 Request permission

Abstract:

We fix a path model for the space of filters of the inverse semigroup $\mathcal {S}_\Lambda$ associated to a left cancellative small category $\Lambda$. Then, we compute its tight groupoid, thus giving a representation of its $C^*$-algebra as a (full) groupoid algebra. Using it, we characterize simplicty for these algebras. Also, we determine amenability of the tight groupoid under mild, reasonable hypotheses.

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