Cup products in Hopf-cyclic cohomology

Masoud Khalkhali; Bahram Rangipour

doi:10.1016/j.crma.2004.10.025

Algebra

Cup products in Hopf-cyclic cohomology

Presented by: Alain Connes

Masoud Khalkhali ¹; Bahram Rangipour ²

¹ Department of Mathematics, University of Western Ontario, London ON, Canada
² Mathematics and Statistics, University of Victoria, Victoria B.C., Canada

Comptes Rendus. Mathématique, Volume 340 (2005) no. 1, pp. 9-14.

Abstract
Résumé

We construct cup products of two different kinds for Hopf-cyclic cohomology. When the Hopf algebra reduces to the ground field our first cup product reduces to Connes' cup product in ordinary cyclic cohomology. The second cup product generalizes Connes–Moscovici's characteristic map for actions of Hopf algebras on algebras.

. Nous construisons deux types de cup-produits pour la cohomologie Hopf-cyclique. Lorsque l'algèbre de Hopf se réduit au corps de base, notre premier cup-produit se réduit au cup-produit de Connes en cohomologie cyclique ordinaire. Le deuxième cup-produit généralise l'application caractéristique de Connes–Moscovici pour l'action des algèbres de Hopf sur les algèbres.

Received: 2004-10-25
Accepted: 2004-10-29
Published online: 2004-12-19

DOI: 10.1016/j.crma.2004.10.025

Author's affiliations:

Masoud Khalkhali ¹; Bahram Rangipour ²

¹ Department of Mathematics, University of Western Ontario, London ON, Canada
² Mathematics and Statistics, University of Victoria, Victoria B.C., Canada

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     title = {Cup products in {Hopf-cyclic} cohomology},
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Masoud Khalkhali; Bahram Rangipour. Cup products in Hopf-cyclic cohomology. Comptes Rendus. Mathématique, Volume 340 (2005) no. 1, pp. 9-14. doi : 10.1016/j.crma.2004.10.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.025/

References
Cited by

[1] R. Akbarpour; M. Khalkhali Equivariant cyclic cohomology of H-algebras, K-Theory, Volume 29 (2003) no. 4, pp. 231-252

[2] A. Connes Noncommutative differential geometry, Inst. Hautes Etudes Sci. Publ. Math., Volume 62 (1985), pp. 257-360

[3] A. Connes Cyclic cohomology and the transverse fundamental class of a foliation, Geometric Methods in Operator Algebras (Kyoto, 1983), Pitman Res. Notes Math. Ser., vol. 123, 1986, pp. 52-144

[4] A. Connes; H. Moscovici Hopf algebras, cyclic cohomology and the transverse index theorem, Commun. Math. Phys., Volume 198 (1998) no. 1, pp. 199-246

[5] A. Connes; H. Moscovici Cyclic cohomology and Hopf algebras, Lett. Math. Phys., Volume 48 (1999) no. 1, pp. 97-108

[6] A. Connes; H. Moscovici Cyclic cohomology and Hopf algebra symmetry, Lett. Math. Phys., Volume 52 (2000) no. 1, pp. 1-28

[7] A. Gorokhovsky Secondary characteristic classes and cyclic cohomology of Hopf algebras, Topology, Volume 41 (2002) no. 5, pp. 993-1016

[8] P.M. Hajac; M. Khalkhali; B. Rangipour; Y. Sommerhäuser Stable anti-Yetter–Drinfeld modules, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 338 (2004) no. 8, pp. 587-590

[9] P.M. Hajac; M. Khalkhali; B. Rangipour; Y. Sommerhäuser Hopf-cyclic homology and cohomology with coefficients, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 338 (2004) no. 9, pp. 667-672

[10] M. Khalkhali On Cartan homotopy formulas in cyclic homology, Manuscripta Math. 94 (1) (1997), pp. 111-132

[11] M. Khalkhali; B. Rangipour A new cyclic module for Hopf algebras, K-Theory, Volume 27 (2002) no. 2, pp. 111-131

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