Cup products in Hopf cyclic cohomology with coefficients in contramodules

Preprint English OPEN
Rangipour, Bahram;
(2010)
  • Subject: Mathematics - K-Theory and Homology | Mathematics - Quantum Algebra
    arxiv: Mathematics::K-Theory and Homology | Mathematics::Quantum Algebra | Mathematics::Category Theory
    mesheuropmc: genetic structures | sense organs

We use stable anti Yetter-Drinfeld contramodules to improve the cup products in Hopf cyclic cohomology. The improvement fixes the lack of functoriality of the cup products previously defined and show that the cup products are sensitive to the coefficients.
  • References (20)
    20 references, page 1 of 2

    [1] Brzezin´ski, T., Hopf-cyclic homology with contramodule coefficients. To appear in Quantum Groups and Noncommutative Spaces, M Marcolli and D Parashar (eds) Vieweg Verlag (MaxPlanck Series), Preprint 2008, arXiv:0806.0389.

    [2] Brzezin´ski, T., Flat connections and (co)modules, New Techniques in Hopf Algebras and Graded Ring Theory, Universa Press, Wetteren, 2007 pp. 35-52. arxiv:math.QA/0608170.

    [3] Connes, A., Noncommutative differential geometry. Inst. Hautes Etudes Sci. Publ. Math. No. 62 (1985), 257-360.

    [4] Connes, A. and Moscovici, H., Background independent geometry and Hopf cyclic cohomology, arXiv:math.QA/0505475.

    [5] Connes, A. and Moscovici, H., Transgressions of the Godbillon-Vey class and Rademacher functions,79-107, Aspects Math., E37, Vieweg, Wiesbaden, 2006.

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

    [7] Crainic, M., Cyclic cohomology of Hopf algebras. J. Pure Appl. Algebra 166 (2002), no. 1-2, 29-66.

    [8] Eilenberg, S. and Moore, J.C., Foundations of relative homological algebra, Mem. Amer. Math. Soc. 55 (1965).

    [9] Getzler, E. and Jones, J. D. S., The cyclic homology of crossed product algebras, J. reine angew. Math. 445 (1993), 163-174.

    [10] Gorokhovsky, A., : Secondary characteristic classes and cyclic cohomology of Hopf algebras, Topology 41(5), 993-1016 (2002)

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