no. 1
Algebra
Cup products in Hopf-cyclic cohomology
[Cup-produits dans la cohomologie Hopf-cyclique]

Présenté par : Alain Connes

Khalkhali, Masoud1 ; Rangipour, Bahram2
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, Tome 340 (2005) no. 1, pp. 9-14.

. 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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.10.025
Khalkhali, Masoud 1 ; Rangipour, Bahram 2

1 Department of Mathematics, University of Western Ontario, London ON, Canada
2 Mathematics and Statistics, University of Victoria, Victoria B.C., Canada 
@article{CRMATH_2005__340_1_9_0,
     author = {Khalkhali, Masoud and Rangipour, Bahram},
     title = {Cup products in {Hopf-cyclic} cohomology},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {9--14},
     publisher = {Elsevier},
     volume = {340},
     number = {1},
     year = {2005},
     doi = {10.1016/j.crma.2004.10.025},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2004.10.025/}
}
TY  - JOUR
AU  - Khalkhali, Masoud
AU  - Rangipour, Bahram
TI  - Cup products in Hopf-cyclic cohomology
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 9
EP  - 14
VL  - 340
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2004.10.025/
DO  - 10.1016/j.crma.2004.10.025
LA  - en
ID  - CRMATH_2005__340_1_9_0
ER  - 
%0 Journal Article
%A Khalkhali, Masoud
%A Rangipour, Bahram
%T Cup products in Hopf-cyclic cohomology
%J Comptes Rendus. Mathématique
%D 2005
%P 9-14
%V 340
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2004.10.025/
%R 10.1016/j.crma.2004.10.025
%G en
%F CRMATH_2005__340_1_9_0
Khalkhali, Masoud; Rangipour, Bahram. Cup products in Hopf-cyclic cohomology. Comptes Rendus. Mathématique, Tome 340 (2005) no. 1, pp. 9-14. doi : 10.1016/j.crma.2004.10.025. http://www.numdam.org/articles/10.1016/j.crma.2004.10.025/

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

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

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

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

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

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

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

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

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

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

Cité par Sources :