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The structure of the Hopf cyclic (co)homology of algebras of smooth functions

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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 theHopf 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.

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References

  1. A. Connes and H. Moscovici, “Hopf algebras, cyclic cohomology and the transverse index theorem,” Comm. Math. Phys. 198 (1), 199–246 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Crainic, “Cyclic cohomology of Hopf algebras,” J. Pure Appl. Algebra 166 (1–2), 29–66 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  3. P. M. Hajac, M. Khalkali, B. Rangipour, and M. Sommerhäuser, “Hopf cyclic homology and cohomology with coefficients.,” C. R. Math. Acad. Sci. Paris 338 (9), 667–672 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Kaygun, “Bialgebra cyclic homology with coefficients,” K-Theory 34 (2), 151–194 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Block and E. Getzler, “Equivariant cyclic homology and equivariant !! a misprint in the original !! differential forms,” Ann. Sci. École Norm. Sup. (4) 27 (4), 493–527 (1994).

    MATH  MathSciNet  Google Scholar 

  6. M. E. Sweedler, Hopf Algebras (W. A. Benjamin, New York, 1969).

    Google Scholar 

  7. J.-L. Loday, Cyclic Homology, in Grundlehren Math. Wiss. (Springer-Verlag, Berlin, 1992), Vol. 301.

  8. P. Baum and P. Schneider, “Equivariant-bivariant Chern character for profinite groups,” K-Theory 25 (4), 313–353 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  9. J. M. Gracia-Bondía, J. C. Várilly, and H. Figueroa, Elements of Noncommutative Geometry (Birkhäuser Boston, Boston, MA, 2001).

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    I. M. Nikonov & G. I. Sharygin

  2. Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia

    G. I. Sharygin

Authors
  1. I. M. Nikonov
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  2. G. I. Sharygin
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Correspondence to I. M. Nikonov.

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Nikonov, I.M., Sharygin, G.I. The structure of the Hopf cyclic (co)homology of algebras of smooth functions. Math Notes 97, 575–587 (2015). https://doi.org/10.1134/S0001434615030281

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  • DOI: https://doi.org/10.1134/S0001434615030281

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