Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T03:01:07.877Z Has data issue: false hasContentIssue false

On codihedral module for *-Hopf algebras

Published online by Cambridge University Press:  04 March 2008

Th. Yu. Popelensky
Affiliation:
[email protected]. of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia
Get access

Abstract

We construct dihedral and reflexive cohomology theories for *-Hopf algebras. This generalizes the Connes–Moscovici construction of cyclic cohomology for Hopf algebras.

Type
Research Article
Copyright
Copyright © ISOPP 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Connes, A., Moscovici, H.Hopf algebras, cyclic cohomology and the transverse index theorem, Comm. Math. Phys. 198 (1998), 199246CrossRefGoogle Scholar
2.Connes, A., Moscovici, H.Cyclic cohomology and Hopf algebras, Lett. Math. Phys. 48 (1999), 97108CrossRefGoogle Scholar
3.Connes, A., Moscovici, H.Cyclic cohomology and Hopf symmetry, Lett. Math. Phys. 52 (2000), 128CrossRefGoogle Scholar
4.Crainic, M.Cyclic cohomology of Hopf algebras, J. Pure Appl. Algebra 166 (2002), 2966CrossRefGoogle Scholar
5.Fiedorowicz, Z., Loday, J.-L.Crossed simplicial groups and their associated homology, Trans of AMS 326, N. 1 (1991), 5787CrossRefGoogle Scholar
6.Hajac, P., Khalkhali, M., Rangipour, B., Sommerhäuser, Y.Hopf-cyclic homology and cohomology with coefficients, C. R. Acad. Sci. Paris, Ser. I, 338 (2004), 667672CrossRefGoogle Scholar
7.Hajac, P., Khalkhali, M., Rangipour, B., Sommerhäuser, Y.Stable anti-Yetter-Drinfeld modules, C. R. Acad. Sci. Paris, Ser. I, 338 (2004) (see also QA/0405005)CrossRefGoogle Scholar
8.Khalkhali, M., Rangipour, B.A new cyclic module for Hopf algebras, K-Theory 27 (2002), 111131CrossRefGoogle Scholar
9.Krasauskas, R., Solovyov, Yu. P.Dihedral homology and Hermitian K-theory of topological spaces, Uspekhi matematicheskih nauk, 1986, T. 41, N. 2, 195196Google Scholar
10.Krasauskas, R., V, S. V., Solovyov, Yu. P.Dihedral homology. Basic notions and construction, Mat. sbornik, 1987, T. 133(175), N. 1(5), 2548Google Scholar
11.Krasauskas, R., Lapin, S. V., Solovyov, Yu. P.Diheral homology and cohomology, Vestnik MGU, Ser. 1. Math. Mech., 1987, N. 4, 2832Google Scholar
12.Krasauskas, R.On cosimplicial groups, Proceedings of XXVII Lithuanian Mathematical Society Conference.Vilnius,VGU, 1986, 910Google Scholar
13.Krasauskas, R.Cosimplicial groups, Lithuanian math. sbornik, 1987, T. 27, N. 1, 8999Google Scholar
14.Loday, J.-L.Homologies dihedrale et quaternionique, Adv. Math. 66 (1987), 119148CrossRefGoogle Scholar
15.Loday, J.-L.Cyclic homology, Springer Verlag, 1998CrossRefGoogle Scholar
16.May, J.P.Simplicial objects in algebraic topology, Princeton, 1967Google Scholar
17.Taillefer, R.Cyclic homology of Hopf algebras, K-Theory 24 (2001), 6985CrossRefGoogle Scholar