2000/08/02 by N.P. Landsman, Landsman, N. P.
Mathematics · #22A22 #46L08 #53D17 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.math-ph/0008005
openalex publication_date 2000/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A theorem of Muhly-Renault-Williams states that if two locally compact groupoids with Haar system are Morita equivalent, then their associated convolution C*-algebras are strongly Morita equivalent. We give a new proof of this theorem for Lie groupoids. Subsequently, we prove a counterpart of this theorem in Poisson geometry: If two Morita equivalent Lie groupoids are s-connected and s-simply connected, then their associated Poisson manifolds (viz. the dual bundles to their Lie algebroids) are Morita equivalent in the sense of P. Xu.