Homotopy theory of Hopf Galois extensions
Annales de l'Institut Fourier, Volume 55 (2005) no. 7, pp. 2521-2550.

We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.

Nous étudions le concept d’équivalence d’homotopie pour les extensions H-galoisiennes où H désigne une algèbre de Hopf. Ceci nous permet de classifier les extensions H-galoisiennes à homotopie près lorsque H est un groupe quantique de Drinfeld-Jimbo.

DOI: 10.5802/aif.2169
Classification: 16W30, 17B37, 55R10, 58B34, 81R50, 81R60
Keywords: Galois extension, Hopf algebra, quantum group, homotopy, noncommutative geometry, principal fibre bundle, Galois extension, Hopf algebra, quantum group, homotopy, noncommutative geometry, principal fibre bundle
Mot clés : extension galoisienne, algèbre de Hopf, groupe quantique, homotopie, géométrie non commutative, fibré principal
Kassel, Christian 1; Schneider, Hans-Jürgen 2

1 Université Louis Pasteur, Institut de Recherche Mathématique Avancée, CNRS, 7 rue René Descartes, 67084 Strasbourg (France)
2 Universität München, Mathematisches Institut, Theresienstr. 39, 80333 Munich (Allemagne)
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Kassel, Christian; Schneider, Hans-Jürgen. Homotopy theory of Hopf Galois extensions. Annales de l'Institut Fourier, Volume 55 (2005) no. 7, pp. 2521-2550. doi : 10.5802/aif.2169. http://www.numdam.org/articles/10.5802/aif.2169/

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