Reconstructing étale groupoids from semigroups
-
Tristan Bice
and
Lisa Orloff Clark
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
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
Funding source: Grantová Agentura České Republiky
Award Identifier / Grant number: 20-31529X
Award Identifier / Grant number: 67985840
Funding statement: The first author is supported by the GAČR project EXPRO 20-31529X and RVO: 67985840. The second author is supported by a Marsden Fund of the Royal Society of New Zealand.
Acknowledgements
The authors would like to thank Astrid an Huef for several conversations and contributions which helped improve the paper. The first author also thanks her for her kind hospitality while he was visiting Victoria University of Wellington in January 2020.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On the topological complexity of manifolds with abelian fundamental group
- Reconstructing étale groupoids from semigroups
- Fiberwise linear differential operators
- Foliations with isolated singularities on Hirzebruch surfaces
- On a stronger reconstruction notion for monoids and clones
- Cochain level May–Steenrod operations
- Commutative L-algebras and measure theory
- Rankin–Selberg integrals for principal series representations of GL(n)
- A simple proof of the generalized Leibniz rule on bounded Euclidean domains
- Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras
- Seshadri constants on some Quot schemes
- Hörmander Fourier multiplier theorems with optimal Besov regularity on multi-parameter Hardy spaces
- On spectral and non-spectral problem for the planar self-similar measures with four element digit sets
- C-minimal topological groups
- Cevian properties in ideal lattices of Abelian ℓ-groups
- Study of twisted Bargmann transform via Bargmann transform
Articles in the same Issue
- Frontmatter
- On the topological complexity of manifolds with abelian fundamental group
- Reconstructing étale groupoids from semigroups
- Fiberwise linear differential operators
- Foliations with isolated singularities on Hirzebruch surfaces
- On a stronger reconstruction notion for monoids and clones
- Cochain level May–Steenrod operations
- Commutative L-algebras and measure theory
- Rankin–Selberg integrals for principal series representations of GL(n)
- A simple proof of the generalized Leibniz rule on bounded Euclidean domains
- Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras
- Seshadri constants on some Quot schemes
- Hörmander Fourier multiplier theorems with optimal Besov regularity on multi-parameter Hardy spaces
- On spectral and non-spectral problem for the planar self-similar measures with four element digit sets
- C-minimal topological groups
- Cevian properties in ideal lattices of Abelian ℓ-groups
- Study of twisted Bargmann transform via Bargmann transform
