We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.
Nous classifions des algèbres intègres finiment engendrées munies d’une action rationnelle d’un groupe réductif connexe avec la propriété suivante : toute sous- algèbre -invariante est finiment engendrée. De plus nous obtenons quelques résultats sur les plongements affines des espaces homogènes.
Keywords: algebraic groups, rational $G$-algebras, quasi-affine homogeneous spaces, affine embeddings
Mot clés : groupes algébriques, $S$-algèbres rationnelles, espaces homogènes quasi-affines, plongements affines
@article{AIF_2003__53_2_379_0,
author = {Arzhantsev, Ivan V.},
title = {Algebras with finitely generated invariant subalgebras},
journal = {Annales de l'Institut Fourier},
pages = {379--398},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {53},
number = {2},
year = {2003},
doi = {10.5802/aif.1947},
mrnumber = {1990001},
zbl = {1099.13500},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1947/}
}
TY - JOUR AU - Arzhantsev, Ivan V. TI - Algebras with finitely generated invariant subalgebras JO - Annales de l'Institut Fourier PY - 2003 SP - 379 EP - 398 VL - 53 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1947/ DO - 10.5802/aif.1947 LA - en ID - AIF_2003__53_2_379_0 ER -
%0 Journal Article %A Arzhantsev, Ivan V. %T Algebras with finitely generated invariant subalgebras %J Annales de l'Institut Fourier %D 2003 %P 379-398 %V 53 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1947/ %R 10.5802/aif.1947 %G en %F AIF_2003__53_2_379_0
Arzhantsev, Ivan V. Algebras with finitely generated invariant subalgebras. Annales de l'Institut Fourier, Volume 53 (2003) no. 2, pp. 379-398. doi : 10.5802/aif.1947. http://www.numdam.org/articles/10.5802/aif.1947/
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