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arXiv · 1906.07487

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

Eduard Ortega·Enrique Pardo
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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 when these algebras are simple. Also, we determine amenability of the tight groupoid under mild, reasonable hypotheses.

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Eduard Ortega, Enrique Pardo. 2019-06-18. The tight groupoid of the inverse semigroups of left cancellative small categories. https://arxiv.org/abs/1906.07487

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