Cyclic cocycles on deformation quantizations and higher index theorems

DOI10.1016/j.aim.2009.10.012zbMath1190.53087arXiv0805.1411OpenAlexW2009903340MaRDI QIDQ962140

Xiang Tang, Hessel Posthuma, Markus J. Pflaum

Publication date: 6 April 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.1411

zbMATH Keywords

symplectic manifoldsWeyl algebraorbifoldsdeformation quantizationscyclic cohomologyAlexander-Spanier cohomologycyclic cocycleshigher index theorems

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Deformation quantization, star products (53D55) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (13)

On the algebraic index for Riemannian étale groupoids ⋮ Characteristic cohomology and observables in higher spin gravity ⋮ Geometry of localized effective theories, exact semi-classical approximation and the algebraic index ⋮ Hochschild Lefschetz class for \(\mathcal D\)-modules ⋮ Deformation quantization with separation of variables of an endomorphism bundle ⋮ A heat kernel proof of the index theorem for deformation quantization ⋮ On the Hochschild homology of proper Lie groupoids ⋮ Chern classes of quantizable coisotropic bundles ⋮ A variant of the Mukai pairing via deformation quantization ⋮ The localized longitudinal index theorem for Lie groupoids and the Van Est map ⋮ Cyclic cohomology of the Weyl algebra ⋮ One-dimensional Chern-Simons theory and the \(\widehat{A}\) genus ⋮ Formality and Kontsevich-Duflo type theorems for Lie pairs

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