Reconstructing a totally disconnected groupoid from its ample semigroup
By R. Exel. 2009
68 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3f43b0e0d2026359cff4dbaebb25893efa2b4007
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In Algebra and Number Theory
- Mark V. Lawson
- Enrique Pardo
- Aidan Sims
- R. Exel
- Ben Steinberg
- L. O. Clark
- Charles Starling
- Daniel Lenz
In Mathematical Physics
- Enrique Pardo
- Mark V. Lawson
- R. Exel
- Ben Steinberg
- Aidan Sims
- L. O. Clark
- Charles Starling
- Daniel Lenz
Citations in the corpus
- A NONCOMMUTATIVE GENERALIZATION OF STONE DUALITY (2009, methodology): “More generally, Paterson [24] used ideas from functional analysis to construct topological groupoids from inverse semigroups and Renault [25] constructed inverse semigroups from topological groupoids using bisections.”
- Simplicity of algebras associated to non-Hausdorff groupoids (2018, background): “Indeed, by [10] every ample groupoid arises this way.”
- Partial transformation groupoids attached to graphs and semigroups (2016, unknown): “The boundary quotient in Exel’s sense (see [9, 10, 11, 13]) is given by ∂C λ(S) := C ∗ λ(S)/ 〈I〉.”
- Pseudogroups and their étale groupoids (2011, background): “Exel’s work [3] is a prime example of this fruitful approach to constructing C∗-algebras.”