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
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.
J. Cuntz, D. Quillen, Cyclic homology and nonsingularity. J. Amer. Math. Soc. 8 (1995), 373–442.
M. Crainic, Cyclic cohomology of Hopf algebras. J. Pure Appl. Algebra 166 (2002), 29–66.
A. Connes, H. Moscovici, Hopf algebras, cyclic cohomology and the transverse index theorem. Commun. Math. Phys. 198 (1998), 199–246.
A. Connes, H. Moscovici, Cyclic cohomology and Hopf algebras. Lett. Math. Phys. 52 (2000), 97–108.
R. Taileffer, Cyclic homology of Hopf algebras. K-Theory 24 (2001), 69–85.
M. Akbarpour, M. Khalkhali, Equivariant cyclic cohomology of Hopf module algebras. J. reine angew. Math. 559 (2003), 137–152.
M. Khalkhali, B. Rangipour, Invariant cyclic homology. K-Theory 28 (2003), 183–205.
M. Khalkhali, B. Rangipour, A new cyclic module for Hopf algebras. K-theory 27 (2002), 111–131.
J.-L. Loday, Cyclic homology. 2-nd Edition, Springer-Verlag, 1998.
M. Khalkhali, B. Rangipour, Cup Products in Hopf-Cyclic Cohomology. C.R. Math. Acad. Sci. Paris 340 (2005), 9–14.
D. Quillen, Chern-Simons forms and cyclic cohomology. The interface of Mathematics and particle Physics, (Oxford, 1988), 117–134.
G. Sharygin, A new construction of characteristic classes for noncommutative algebraic principal bundles. Banach Center Publ. 61 (2003), 219–230.
I. Nikonov, G. Sharygin, Pairings in Hopf-type cyclic cohomology with coefficients. (in preparation)
D. Quillen, Algebra cochains and cyclic cohomology. Publ. Math. I.H.E.S. 68 (1989), 139–174.
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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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DOI: https://doi.org/10.1007/978-3-7643-7687-1_10
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