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Cyclic Cohomology of Corings

Published online by Cambridge University Press:  14 November 2008

Bahram Rangipour
Bahram Rangipour
Affiliation:
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, CANADA, E3B 5A3, bahram@unb.ca.
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Abstract

We define cyclic cohomology of corings over not necessarily commutative algebras. Our method is a generalization of Hopf-cyclic cohomology obtained by replacing coalgebras and Hopf algebras with corings and para-Hopf algebroids, respectively. We also study the dual of this theory whose cyclic cohomology, in contrast with the case of algebras and coalgebras, is not trivial.

Keywords

Coringspara Hopf algebroidscyclic objectscyclic cohomology
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 1 , August 2009 , pp. 193 - 207
Copyright
Copyright © ISOPP 2008

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References

1.Brzezinski, T., and Wisbauer, R., Corings and comodules. London Mathematical Society Lecture Note Series 309. Cambridge University Press, Cambridge, 2003Google Scholar
2.Brzezinski, T., Militaru, G., Bialgebroids, ×A-bialgebras and duality. J. Algebra 251 (2002), 279–294Google Scholar
3.Connes, A., Noncommutative differential geometry. Inst. Hautes Études Sci. Publ. Math. 62 (1985), 257–360CrossRefGoogle Scholar
4.Connes, A., Cohomologie cyclique et foncteurs Extn. C. R. Acad. Sci. Paris Ser. I Math. 296 (23) (1983), 953–958Google Scholar
5.Connes, A. and Moscovici, H.,Modular Hecke algebras and their Hopf symmetry, Moscow Math. Journal 4 (2004), 67–130CrossRefGoogle Scholar
6.Connes, A. and Moscovici, H., Differential cyclic cohomology and Hopf algebraic structures in transverse geometry. Essays on geometry and related topics, Vol. 1, 2, 217–255, Monogr. Enseign. Math. 38, Enseignement Math., Geneva, 2001Google Scholar
7.Connes, A. and Moscovici, H., Hopf algebras, Cyclic Cohomology and the transverse index theorem., Comm.Math. Phys. 198 (1) (1998), 199–246CrossRefGoogle Scholar
8.Guzman, F., Cointegrations, relative cohomology for comodules, and coseparable corings. J. Algebra 126 (1) (1989), 211–224Google Scholar
9.Hajac, P. M., Khalkhali, M., Rangipour, B., and Sommerhäuser, Y., Hopf-cyclic homology and cohomology with coefficients. C. R. Math. Acad. Sci. Paris 338 (2004), no. 9, 667–672.CrossRefGoogle Scholar
10.Khalkhali, M. and Rangipour, B., A note on cyclic duality and Hopf algebras, Communications in Algebra 33 (3) (2005), 763–773CrossRefGoogle Scholar
11.Khalkhali, M. and Rangipour, B.Para-Hopf algebroids and their cyclic cohomology. Lett. Math. Phys. 70 (3) (2004), 259–272CrossRefGoogle Scholar
12.Khalkhali, M. and Rangipour, B., Invariant cyclic homology. K-Theory 28 (2) (2003), 183-205Google Scholar
13.Khalkhali, M. and Rangipour, B.A New Cyclic Module for Hopf Algebras. K-Theory 27 (2) (2002), 111–131CrossRefGoogle Scholar