Nous étudions le concept d’équivalence d’homotopie pour les extensions -galoisiennes où désigne une algèbre de Hopf. Ceci nous permet de classifier les extensions -galoisiennes à homotopie près lorsque 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 -Galois extensions up to homotopy equivalence in the case when is a Drinfeld-Jimbo quantum group.
Classification : 16W30, 17B37, 55R10, 58B34, 81R50, 81R60
Mots clés : extension galoisienne, algèbre de Hopf, groupe quantique, homotopie, géométrie non commutative, fibré principal
@article{AIF_2005__55_7_2521_0, 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'institut Fourier}, volume = {55}, number = {7}, year = {2005}, doi = {10.5802/aif.2169}, zbl = {1090.16019}, mrnumber = {2207392}, language = {en}, url = {www.numdam.org/item/AIF_2005__55_7_2521_0/} }
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/item/AIF_2005__55_7_2521_0/
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