Reconstructing étale groupoids from semigroups
Abstract We unify various étale groupoid reconstruction theorems such as the following: • Kumjian and Renault’s reconstruction from a groupoid C*-algebra; • Exel’s reconstruction from an ample inverse semigroup; • Steinberg’s reconstruction from a groupoid ring; • Choi, Gardella and Thiel’s reconstruction from a groupoid L p {L^{p}} -algebra. We do this by working with certain bumpy semigroups S of functions defined on an étale groupoid G. The semigroup structure of S together with the diagonal subsemigroup D then yields a natural domination relation ≺ {\prec} on S. The groupoid of ≺ {\prec} -ultrafilters is then isomorphic to the original groupoid G.
2012 ◽
Vol 05
(02)
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pp. 1250029
2013 ◽
Vol 94
(2)
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pp. 234-256
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2010 ◽
Vol 53
(3)
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pp. 765-785
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2006 ◽
Vol 10
(6)
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pp. 1539-1548
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2018 ◽
Vol 104
(3)
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pp. 403-411
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