A nonlinearizable action of S 3 on ℂ 4
[Une action non linéarisable de S 3 sur ℂ 4 ]
Freudenburg, Gene ; Moser-Jauslin, Lucy
Annales de l'Institut Fourier, Tome 52 (2002), p. 133-143 / Harvested from Numdam
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Nous construisons une action algébrique non linéarisable (i.e. pas conjuguée à une action linéaire) du groupe S 3 des permutations de 3 éléments sur l’espace affine complexe de dimension quatre. Plus généralement, cette action peut être utilisée pour construire des actions non linéarisables de S 3 sur ℂ n pour tout entier n≥4.

The main purpose of this article is to give an explicit algebraic action of the group S 3 of permutations of 3 elements on affine four-dimensional complex space which is not conjugate to a linear action.

Publié le : 2002-01-01
DOI : https://doi.org/10.5802/aif.1879
Classification:  14R20,  13A50
Mots clés: actions non linéarisables, fibrés vectoriels équivariants, invariants 
@article{AIF_2002__52_1_133_0,
     author = {Freudenburg, Gene and Moser-Jauslin, Lucy},
     title = {A nonlinearizable action of $S\_3$ on ${\mathbb {C}}^4$},
     journal = {Annales de l'Institut Fourier},
     volume = {52},
     year = {2002},
     pages = {133-143},
     doi = {10.5802/aif.1879},
     mrnumber = {1881573},
     zbl = {1028.14019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2002__52_1_133_0}
}

Freudenburg, Gene; Moser-Jauslin, Lucy. A nonlinearizable action of $S_3$ on ${\mathbb {C}}^4$. Annales de l'Institut Fourier, Tome 52 (2002) pp. 133-143. doi : 10.5802/aif.1879. http://gdmltest.u-ga.fr/item/AIF_2002__52_1_133_0/

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