RENAULT'S EQUIVALENCE THEOREM FOR GROUPOID CROSSED PRODUCTS

By P. Muhly, Dana P. Williams. 2007

89 citations recorded by the source corpus.

We provide an exposition and proof of Renault's equivalence theo- rem for crossed products by locally Hausdorff, locally compact groupoids. Our approach stresses the bundle approach, concrete imprimitivity bimodules and is a preamble to a detailed treatment of the Brauer semigroup for a locally Hausdorff, locally compact groupoid.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/519817fb95a839d684d7f1a7b11fda25c1cc95a5

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In Algebra and Number Theory

1. Ben Steinberg
2. Aidan Sims
3. L. O. Clark
4. David Milan
5. J. Brown
6. Xin Li
7. Cynthia Farthing
8. R. Exel

In Mathematical Physics

1. Aidan Sims
2. Ben Steinberg
3. L. O. Clark
4. David Milan
5. J. Brown
6. Xin Li
7. Cynthia Farthing
8. R. Exel

Citations in the corpus

• Nuclearity of semigroup C*-algebras and the connection to amenability (2012, methodology): “It is straightforward to check that this family (α(S)[s,χ])[s,χ]∈G(S) gives rise to the desired groupoid dynamical system in the sense of [Muh-Wil], § 4.”
• Simplicity of algebras associated to étale groupoids (2012, background): “There is a representation (in the sense of [22]) of G on the Borel Hilbert bundle G×C determined by Uγ : (s(γ), z) 7→ (r(γ), z).”
• ON INVERSE SEMIGROUP C ∗ -ALGEBRAS AND CROSSED PRODUCTS (2011, background): “A theorem of Renault [23] (in the non-Hausdorff case), see also [20], implies that if G and H are Morita equivalent locally compact groupoids, then C .”