no. 2
Algebras with finitely generated invariant subalgebras
[Algèbres dont toute sous-algèbre invariante est finiment engendrée]
Arzhantsev, Ivan V.1
1 Moscow State University, Department of Mathematics and Mechanics, Chair of Higher Algebra, Vorobievy Gory, GSP-2, Moscow 119992 (Russie)
Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 379-398.

Nous classifions des algèbres intègres finiment engendrées munies d’une action rationnelle d’un groupe réductif connexe G avec la propriété suivante : toute sous- algèbre G-invariante est finiment engendrée. De plus nous obtenons quelques résultats sur les plongements affines des espaces homogènes.

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.

DOI : 10.5802/aif.1947
Classification : 13A50, 13E15, 14L17, 14L30, 14M17, 14R20
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
Arzhantsev, Ivan V. 1

1 Moscow State University, Department of Mathematics and Mechanics, Chair of Higher Algebra, Vorobievy Gory, GSP-2, Moscow 119992 (Russie) 
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Arzhantsev, Ivan V. Algebras with finitely generated invariant subalgebras. Annales de l'Institut Fourier, Tome 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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