Algebras with finitely generated invariant subalgebras
Annales de l'Institut Fourier, Volume 53 (2003) no. 2, p. 379-398

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.

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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