Comptes Rendus
no. 8
Algebra/Topology
Stable anti-Yetter–Drinfeld modules
[Modules anti-Yetter–Drinfeld stables]

Présenté par : Alain Connes

Piotr M. Hajac1, 2 ; Masoud Khalkhali3 ; Bahram Rangipour3 ; Yorck Sommerhäuser4
1 Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, Warszawa, 00-956 Poland
2 Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski, ul. Hoża 74, Warszawa, 00-682 Poland
3 Department of Mathematics, University of Western Ontario, London ON, Canada
4 Mathematisches Institut, Universität München, Theresienstr. 39, 80333 München, Germany
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 587-590.

Nous définissons et étudions une classe de modules enlacés (modules anti-Yetter–Drinfeld stables) qui servent de coefficients pour l'homologie et la cohomologie Hopf-cyclique. En particulier, nous expliquons leurs liens avec les modules de Yetter–Drinfeld et les doublets de Drinfeld. Parmi les sources d'exemples de modules anti-Yetter–Drinfeld stables, nous trouvons des extensions de Hopf–Galois munies d'une version transposée de l'action de Miyashita–Ulbrich.

We define and study a class of entwined modules (stable anti-Yetter–Drinfeld modules) that serve as coefficients for the Hopf-cyclic homology and cohomology. In particular, we explain their relationship with Yetter–Drinfeld modules and Drinfeld doubles. Among sources of examples of stable anti-Yetter–Drinfeld modules, we find Hopf–Galois extensions with a flipped version of the Miyashita–Ulbrich action.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2003.11.037
Piotr M. Hajac 1, 2 ; Masoud Khalkhali 3 ; Bahram Rangipour 3 ; Yorck Sommerhäuser 4

1 Instytut Matematyczny, Polska Akademia Nauk, ul. Śniadeckich 8, Warszawa, 00-956 Poland
2 Katedra Metod Matematycznych Fizyki, Uniwersytet Warszawski, ul. Hoża 74, Warszawa, 00-682 Poland
3 Department of Mathematics, University of Western Ontario, London ON, Canada
4 Mathematisches Institut, Universität München, Theresienstr. 39, 80333 München, Germany 
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     title = {Stable {anti-Yetter{\textendash}Drinfeld} modules},
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     pages = {587--590},
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Piotr M. Hajac; Masoud Khalkhali; Bahram Rangipour; Yorck Sommerhäuser. Stable anti-Yetter–Drinfeld modules. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 587-590. doi : 10.1016/j.crma.2003.11.037. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.11.037/

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