Reconstructing a totally disconnected groupoid from its ample semigroup
classification
🧮 math.OA
math.DS
keywords
ampledisconnectedgroupoidsemigrouptotallyalgebraiccountableetale
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We show that a (not necessarily Hausdorff) etale, second countable groupoid G with totally disconnected unit space may be reconstructed solely from the algebraic structure of its ample semigroup S. We also show that C*(G) possesses a universal property related to tight representations of S.
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