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The tight groupoid of the inverse semigroups of left cancellative small categories (1906.07487v1)
Published 18 Jun 2019 in math.OA and math.RA
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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