2003/05/18 by Frédéric Cadet, Frederic Cadet, Cadet, Frederic
Mathematics · Physics and Astronomy · #46L65 #46LXX #52D17 #53D20 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA #msc:46L65 #msc:46LXX #msc:52D17 #msc:53D20
paper · pdf · doi:10.48550/arxiv.math/0305261
20 pages
openalex publication_date 2003/05/18 · arxiv created 2003/05/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the framework of C*-algebraic deformation quantization we propose a notion of deformation groupoid which could apply to known examples e.g. Connes' tangent groupoid of a manifold, its generalisation by Landsman and Ramazan, Rieffel's noncommutative torus, and even Landi's noncommutative 4-sphere. We construct such groupoid for a wide class of Tn-spaces, that generalizes the one given for Cn by Bellissard and Vittot. In particular, using the geometric properties of the moment map discovered in the '80s by Atiyah, Delzant, Guillemin and Sternberg, it provides a \cstar-algebraic deformation quantization for all toric manifolds, including the 2-sphere and all complex projective spaces.