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On the Hopf-type Cyclic Cohomology with Coefficients

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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.

The first author was supported by the grant RFFI 05-01-00923 and the Presidential grant NSh- 1988.2003.1

The second author was partly supported by the grant RFFI 04-01-00702.

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References

  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.

    MATH  MathSciNet  Google Scholar 

  2. J. Cuntz, D. Quillen, Cyclic homology and nonsingularity. J. Amer. Math. Soc. 8 (1995), 373–442.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Connes, H. Moscovici, Cyclic cohomology and Hopf algebras. Lett. Math. Phys. 52 (2000), 97–108.

    Article  MathSciNet  Google Scholar 

  6. R. Taileffer, Cyclic homology of Hopf algebras. K-Theory 24 (2001), 69–85.

    Article  MathSciNet  Google Scholar 

  7. M. Akbarpour, M. Khalkhali, Equivariant cyclic cohomology of Hopf module algebras. J. reine angew. Math. 559 (2003), 137–152.

    MATH  MathSciNet  Google Scholar 

  8. M. Khalkhali, B. Rangipour, Invariant cyclic homology. K-Theory 28 (2003), 183–205.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Khalkhali, B. Rangipour, A new cyclic module for Hopf algebras. K-theory 27 (2002), 111–131.

    Article  MATH  MathSciNet  Google Scholar 

  10. J.-L. Loday, Cyclic homology. 2-nd Edition, Springer-Verlag, 1998.

    Google Scholar 

  11. M. Khalkhali, B. Rangipour, Cup Products in Hopf-Cyclic Cohomology. C.R. Math. Acad. Sci. Paris 340 (2005), 9–14.

    MATH  MathSciNet  Google Scholar 

  12. D. Quillen, Chern-Simons forms and cyclic cohomology. The interface of Mathematics and particle Physics, (Oxford, 1988), 117–134.

    Google Scholar 

  13. G. Sharygin, A new construction of characteristic classes for noncommutative algebraic principal bundles. Banach Center Publ. 61 (2003), 219–230.

    Article  MATH  MathSciNet  Google Scholar 

  14. I. Nikonov, G. Sharygin, Pairings in Hopf-type cyclic cohomology with coefficients. (in preparation)

    Google Scholar 

  15. D. Quillen, Algebra cochains and cyclic cohomology. Publ. Math. I.H.E.S. 68 (1989), 139–174.

    Google Scholar 

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Nikonov, I.M., Sharygin, G.I. (2006). On the Hopf-type Cyclic Cohomology with Coefficients. In: Bojarski, B., Mishchenko, A.S., Troitsky, E.V., Weber, A. (eds) C*-algebras and Elliptic Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7687-1_10

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