Homotopy theory of Hopf Galois extensions

Kassel, Christian; Schneider, Hans-Jürgen

doi:10.5802/aif.2169

Homotopy theory of Hopf Galois extensions
[Homotopie des extensions de Hopf Galois]

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)

Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2521-2550.

Résumé
Abstract

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.

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.

MR Zbl

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

Affiliations des auteurs :

Kassel, Christian ¹ ; Schneider, Hans-Jürgen ²

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     author = {Kassel, Christian and Schneider, Hans-J\"urgen},
     title = {Homotopy theory of {Hopf} {Galois} extensions},
     journal = {Annales de l'Institut Fourier},
     pages = {2521--2550},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {55},
     number = {7},
     year = {2005},
     doi = {10.5802/aif.2169},
     mrnumber = {2207392},
     zbl = {1090.16019},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2169/}
}

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Kassel, Christian; Schneider, Hans-Jürgen. Homotopy theory of Hopf Galois extensions. Annales de l'Institut Fourier, Tome 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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