Algebras with finitely generated invariant subalgebras  [ Algèbres dont toute sous-algèbre invariante est finiment engendrée ]
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 : https://doi.org/10.5802/aif.1947
Classification : 13A50,  13E15,  14L17,  14L30,  14M17,  14R20
Mots 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'institut Fourier},
     volume = {53},
     number = {2},
     year = {2003},
     doi = {10.5802/aif.1947},
     mrnumber = {1990001},
     zbl = {1099.13500},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2003__53_2_379_0/}
}
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. https://aif.centre-mersenne.org/item/AIF_2003__53_2_379_0/

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