Algebras with finitely generated invariant subalgebras

Arzhantsev, Ivan V.

Arzhantsev, Ivan V.

Annales de l'Institut Fourier, Volume 53 (2003) no. 2, p. 379-398

Abstract
Résumé

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 $G$ 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.

MR 1990001 | Zbl 1099.13500

DOI : https://doi.org/10.5802/aif.1947
Classification: 13A50, 13E15, 14L17, 14L30, 14M17, 14R20
Keywords: algebraic groups, rational

G

-algebras, quasi-affine homogeneous spaces, affine embeddings

@article{AIF_2003__53_2_379_0,
     author = {Arzhantsev, Ivan V.},
     title = {Algebras with finitely generated invariant subalgebras},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {2},
     year = {2003},
     pages = {379-398},
     doi = {10.5802/aif.1947},
     zbl = {1099.13500},
     mrnumber = {1990001},
     language = {en},
     url = {http://www.numdam.org/item/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/item/AIF_2003__53_2_379_0/

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