Algebra/Topology
Stable anti-Yetter–Drinfeld modules
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 587-590.

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.

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.

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DOI: 10.1016/j.crma.2003.11.037
Hajac, Piotr M. 1, 2; Khalkhali, Masoud 3; Rangipour, Bahram 3; Sommerhäuser, Yorck 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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Hajac, Piotr M.; Khalkhali, Masoud; Rangipour, Bahram; Sommerhäuser, Yorck. Stable anti-Yetter–Drinfeld modules. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 587-590. doi : 10.1016/j.crma.2003.11.037. http://www.numdam.org/articles/10.1016/j.crma.2003.11.037/

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