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Homology of complete symbols and noncommutative geometry

  • Conference paper
Quantization of Singular Symplectic Quotients

Part of the book series: Progress in Mathematics ((PM,volume 198))

Abstract

We identify the periodic cyclic homology of the algebra of complete symbols on a differential groupoidGin terms of the cohomology ofS* (G), the cosphere bundle ofA(G), whereA(G)is the Lie algebroid ofG.We also relate the Hochschild homology of this algebra with the homogeneous Poisson homology of the space, A* (G) \ 0 ≅ S* (G) × (0, ∞), the dual ofA(G)with the zero section removed. We use then these results to compute the Hochschild and cyclic homologies of the algebras of complete symbols associated with manifolds with corners, when the corresponding Lie algebroid is rationally isomorphic to the tangent bundle.

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Author information

Authors and Affiliations

  1. Pennsylvania State University and Inst. Desargues, Lyon, France

    Moulay-Tahar Benameur

  2. Inst. Desargues and Pennsylvania State University, University Park, PA, 16802

    Victor Nistor

Authors
  1. Moulay-Tahar Benameur
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  2. Victor Nistor
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Editor information

Editors and Affiliations

  1. Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    N. P. Landsman

  2. Mathematisch-Naturwissenschaftliche Fakultät II Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    M. Pflaum

  3. Fakultät für Mathematik und Informatik, Universität Mannheim, D7, 27, 68131, Mannheim, Germany

    M. Schlichenmaier

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© 2001 Springer Basel AG

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Benameur, MT., Nistor, V. (2001). Homology of complete symbols and noncommutative geometry. In: Landsman, N.P., Pflaum, M., Schlichenmaier, M. (eds) Quantization of Singular Symplectic Quotients. Progress in Mathematics, vol 198. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8364-1_2

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  • DOI: https://doi.org/10.1007/978-3-0348-8364-1_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9535-4

  • Online ISBN: 978-3-0348-8364-1

  • eBook Packages: Springer Book Archive

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