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.
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.
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
@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{\textquoteright}institut Fourier}, volume = {55}, number = {7}, year = {2005}, doi = {10.5802/aif.2169}, mrnumber = {2207392}, zbl = {1090.16019}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2169/} }
TY - JOUR AU - Kassel, Christian AU - Schneider, Hans-Jürgen TI - Homotopy theory of Hopf Galois extensions JO - Annales de l'Institut Fourier PY - 2005 SP - 2521 EP - 2550 VL - 55 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2169/ DO - 10.5802/aif.2169 LA - en ID - AIF_2005__55_7_2521_0 ER -
%0 Journal Article %A Kassel, Christian %A Schneider, Hans-Jürgen %T Homotopy theory of Hopf Galois extensions %J Annales de l'Institut Fourier %D 2005 %P 2521-2550 %V 55 %N 7 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2169/ %R 10.5802/aif.2169 %G en %F AIF_2005__55_7_2521_0
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://archive.numdam.org/articles/10.5802/aif.2169/
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