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EQUIVARIANT ALGEBRAIC INDEX THEOREM

Part of: Applied homological algebra and category theory Homological algebra $K$-theory and operator algebras Pseudogroups, differentiable groupoids and general structures on manifolds

Published online by Cambridge University Press:  27 August 2019

Alexander Gorokhovsky ,
Niek de Kleijn  and
Ryszard Nest Open the ORCID record for Ryszard Nest [Opens in a new window]
Alexander Gorokhovsky
Affiliation:
Kobenhavns Universitet Det Natur-og Biovidenskabelige Fakultet, Mathematics, Universitetsparken 5, 2100, Copenhagen, Denmark (rnest@math.ku.dk)
Niek de Kleijn
Affiliation:
Kobenhavns Universitet Det Natur-og Biovidenskabelige Fakultet, Mathematics, Universitetsparken 5, 2100, Copenhagen, Denmark (rnest@math.ku.dk)
Ryszard Nest
Affiliation:
Kobenhavns Universitet Det Natur-og Biovidenskabelige Fakultet, Mathematics, Universitetsparken 5, 2100, Copenhagen, Denmark (rnest@math.ku.dk)
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Abstract

We prove a $\unicode[STIX]{x1D6E4}$-equivariant version of the algebraic index theorem, where $\unicode[STIX]{x1D6E4}$ is a discrete group of automorphisms of a formal deformation of a symplectic manifold. The particular cases of this result are the algebraic version of the transversal index theorem related to the theorem of A. Connes and H. Moscovici for hypo-elliptic operators and the index theorem for the extension of the algebra of pseudodifferential operators by a group of diffeomorphisms of the underlying manifold due to A. Savin, B. Sternin, E. Schrohe and D. Perrot.

Keywords

deformation quantizationindex theorem

MSC classification

Primary: 19K56: Index theory 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
Secondary: 18G30: Simplicial sets, simplicial objects (in a category) 55U10: Simplicial sets and complexes
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 3 , May 2021 , pp. 929 - 955
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Copyright
© Cambridge University Press 2019

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Footnotes

Alexander Gorokhovsky was partially supported by an NSF grant. Niek de Kleijn and Ryszard Nest were supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92). Niek de Kleijn was also partially supported by the IAP ‘Dygest’ of the Belgian Science Policy.

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