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Uniqueness of pairings in Hopf-cyclic cohomology

Published online by Cambridge University Press:  21 January 2010

Atabey Kaygun
Atabey Kaygun
Affiliation:
Department of Mathematics and Computer Science, Bahçeşehir University, Çirağan Caddesi, Beşiktaş 34353 İstanbul, TURKEY, [email protected].
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Abstract

We show that all pairings defined in the literature extending the Connes-Moscovici characteristic map in Hopf cyclic cohomology are isomorphic as natural transformations of derived double functors.

Keywords

Hopf algebracyclic cohomologycup productderived category
Type
Research Article
Information
Journal of K-Theory , Volume 6 , Issue 1 , August 2010 , pp. 1 - 21
Copyright
Copyright © ISOPP 2010

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References

1.Connes, A.. Cohomologie cyclique et foncteurs Extn. C. R. Acad. Sci. Paris Sér. I Math. 296(23):953–958, 1983.Google Scholar
2.Connes, A.. Noncommutative differential geometry. Inst. Hautes Études Sci. Publ. Math. 62:257–360, 1985.Google Scholar
3.Connes, A.. Noncommutative geometry . Academic Press Inc., 1994 (Also available online at http://www.alainconnes.org/docs/book94bigpdf.pdf).Google Scholar
4.Connes, A. and Moscovici, H.. Hopf algebras, cyclic cohomology and transverse index theorem. Comm. Math. Phys. 198:199–246, 1998.CrossRefGoogle Scholar
5.Connes, A. and Moscovici, H.. Cyclic cohomology and Hopf algebras. Lett. Math. Phys. 48(1):97–108, 1999. Moshé Flato (1937–1998).Google Scholar
6.Connes, A. and Moscovici, H.. Cyclic cohomology and Hopf algebra symmetry. Lett. Math. Phys. 52(1):1–28, 2000.Google Scholar
7.Crainic, M.. Cyclic cohomology of Hopf algebras. J. Pure Appl. Algebra. 166(1–2):29–66, 2002.Google Scholar
8.Cuntz, J. and Quillen, D.. Cyclic homology and nonsingularity. J. Amer. Math. Soc. 8(2):373–442, 1995.CrossRefGoogle Scholar
9.Dold, A. and Puppe, D.. Homologie nicht-additiver Funktoren. Anwendungen. Ann. Inst. Fourier Grenoble. 11:201–312, 1961.Google Scholar
10.Gorokhovsky, A.. Secondary characteristic classes and cyclic cohomology of Hopf algebras. Topology. 41(5):993–1016, 2002.CrossRefGoogle Scholar
11.Hajac, P. M., Khalkhali, M., Rangipour, B., and Sommerhäuser, Y.. Hopf-cyclic homology and cohomology with coefficients. C. R. Math. Acad. Sci. Paris. 338(9):667–672, 2004.CrossRefGoogle Scholar
12.Hajac, P. M., Khalkhali, M., Rangipour, B., and Sommerhäuser, Y.. Stable anti-Yetter-Drinfeld modules. C. R. Math Acad. Sci. Paris. 338(8):587–590, 2004.CrossRefGoogle Scholar
13.Hochschild, G.. Relative homological algebra. Trans. Amer. Math. Soc. 82:246–269, 1956.Google Scholar
14.Jones, J. D. S. and Kassel, C.. Bivariant cyclic theory. K-Theory. 3(4):339–365, 1989.Google Scholar
15.Kaygun, A.. Products in Hopf-cyclic cohomology. Homology, Homotopy and Applications. 10(2):115–133, 2008.CrossRefGoogle Scholar
16.Kaygun, A. and Khalkhali, M.. Bivariant Hopf cyclic cohomology. Preprint at arXiv:math/0606341 [math.KT].Google Scholar
17.Keller, B.. On differential graded categories. In International Congress of Mathematicians. Vol. II, pages 151–190. Eur. Math. Soc., Zürich, 2006.Google Scholar
18.Khalkhali, M. and Rangipour, B.. Cup products in Hopf-cyclic cohomology. C. R. Math. Acad. Sci. Paris. 340(1):9–14, 2005.Google Scholar
19.MacLane, S.. Homology, Die Grundlehren der mathematischen Wissenschaften 114. Academic Press Inc., New York, 1963.Google Scholar
20.Nistor, V.. A bivariant Chern-Connes character. Ann. of Math. 138(3):555–590, 1993.Google Scholar
21.Quillen, D.. Bivariant cyclic cohomology and models for cyclic homology types. J. Pure Appl. Algebra. 101(1):1–33, 1995.Google Scholar
22.Rangipour, B.. Cup products in Hopf cyclic cohomology via cyclic modules I. Preprint at arXiv:0710.2623v1/ [math.KT].Google Scholar
23.Sharygin, G. I. and Nikonov, I.. Pairings in Hopf-cyclic cohomology of algebras and coalgebras with coefficients. Preprint at arXiv:math/0610615v1 [math.KT].Google Scholar
24.Weibel, C. A.. An Introduction to Homological Algebra. Cambridge Studies in Advanced Mathematics 38. Cambridge University Press, 1995.Google Scholar
25.Wodzicki, M.. Excision in cyclic homology and in rational algebraic K-Theory. Ann. of Math. 129(3):591–639, 1989.CrossRefGoogle Scholar