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Mat. Zametki, 2015, Volume 97, Issue 4, Pages 566–582 (Mi mz9354)  

This article is cited in 1 scientific paper (total in 1 paper)

The Structure of the Hopf Cyclic (Co)Homology of Algebras of Smooth Functions

I. M. Nikonova, G. I. Sharyginab

a M. V. Lomonosov Moscow State University
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center), Moscow

Abstract: The paper discusses the structure of the Hopf cyclic homology and cohomology of the algebra of smooth functions on a manifold provided that the algebra is endowed with an action or a coaction of the algebra of Hopf functions on a finite or compact group or of the Hopf algebra dual to it. In both cases, an analog of the Connes–Hochschild–Kostant–Rosenberg theorem describing the structure of Hopf cyclic cohomology in terms of equivariant cohomology and other more geometric cohomology groups is proved.

Keywords: Hopf cyclic homology with coefficients, Hopf cyclic cohomology with coefficients, algebra of smooth functions on a manifold, Hopf algebra of functions on a group, Hopf cyclic complex, equivariant cohomology, module of sections.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00007-a
Ministry of Education and Science of the Russian Federation НШ-581.2014.1
This work was supported by the Russian Foundation for Basic Research (grant no. 14-01-00007-a) and by the program “Leading Scientific Schools” (grant no. NSh-581.2014.1).


DOI: https://doi.org/10.4213/mzm9354

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English version:
Mathematical Notes, 2015, 97:4, 575–587

Bibliographic databases:

UDC: 514.7
Received: 03.03.2012
Revised: 22.11.2014

Citation: I. M. Nikonov, G. I. Sharygin, “The Structure of the Hopf Cyclic (Co)Homology of Algebras of Smooth Functions”, Mat. Zametki, 97:4 (2015), 566–582; Math. Notes, 97:4 (2015), 575–587

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Nikonov I.M., Sharygin G.I., “Hopf Cyclic Cohomology and Chern Character of Equivariant K-Theories”, Russ. J. Math. Phys., 22:3 (2015), 379–388  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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