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On the Hopf-type Cyclic Cohomology with Coefficients

  • I. M. Nikonov
  • G. I. Sharygin
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

In this note we discuss the Hopf-type cyclic cohomology with coefficients, introduced in the paper [1]: we calculate it in a couple of interesting examples and propose a general construction of coupling between algebraic and coalgebraic version of such cohomology, taking values in the usual cyclic cohomology of an algebra.

Keywords

Cyclic homology Hopf algebras Weil complex 

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References

  1. [1]
    P.M. Hajac, M. Khalkali, B. Rangipour, M. Sommerhäuser, Hopf-cyclic homology and cohomology with coefficients. C.R. Math. Acad. Sci. Paris 338 (2004), 667–672.zbMATHMathSciNetGoogle Scholar
  2. [2]
    J. Cuntz, D. Quillen, Cyclic homology and nonsingularity. J. Amer. Math. Soc. 8 (1995), 373–442.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    M. Crainic, Cyclic cohomology of Hopf algebras. J. Pure Appl. Algebra 166 (2002), 29–66.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    A. Connes, H. Moscovici, Hopf algebras, cyclic cohomology and the transverse index theorem. Commun. Math. Phys. 198 (1998), 199–246.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    A. Connes, H. Moscovici, Cyclic cohomology and Hopf algebras. Lett. Math. Phys. 52 (2000), 97–108.MathSciNetCrossRefGoogle Scholar
  6. [6]
    R. Taileffer, Cyclic homology of Hopf algebras. K-Theory 24 (2001), 69–85.MathSciNetCrossRefGoogle Scholar
  7. [7]
    M. Akbarpour, M. Khalkhali, Equivariant cyclic cohomology of Hopf module algebras. J. reine angew. Math. 559 (2003), 137–152.zbMATHMathSciNetGoogle Scholar
  8. [8]
    M. Khalkhali, B. Rangipour, Invariant cyclic homology. K-Theory 28 (2003), 183–205.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    M. Khalkhali, B. Rangipour, A new cyclic module for Hopf algebras. K-theory 27 (2002), 111–131.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    J.-L. Loday, Cyclic homology. 2-nd Edition, Springer-Verlag, 1998.Google Scholar
  11. [11]
    M. Khalkhali, B. Rangipour, Cup Products in Hopf-Cyclic Cohomology. C.R. Math. Acad. Sci. Paris 340 (2005), 9–14.zbMATHMathSciNetGoogle Scholar
  12. [12]
    D. Quillen, Chern-Simons forms and cyclic cohomology. The interface of Mathematics and particle Physics, (Oxford, 1988), 117–134.Google Scholar
  13. [13]
    G. Sharygin, A new construction of characteristic classes for noncommutative algebraic principal bundles. Banach Center Publ. 61 (2003), 219–230.zbMATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    I. Nikonov, G. Sharygin, Pairings in Hopf-type cyclic cohomology with coefficients. (in preparation)Google Scholar
  15. [15]
    D. Quillen, Algebra cochains and cyclic cohomology. Publ. Math. I.H.E.S. 68 (1989), 139–174.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • I. M. Nikonov
    • 1
  • G. I. Sharygin
    • 2
  1. 1.Dept. of Differential GeometryMoscow State UniversityMoscowRussia
  2. 2.ITEPMoscowRussia

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