A nonlinearizable action of $S_3$ on ${\mathbb {C}}^4$

Freudenburg, Gene; Moser-Jauslin, Lucy

doi:10.5802/aif.1879

A nonlinearizable action of

S_{3}

ℂ^{4}

[Une action non linéarisable de

S_{3}

sur

ℂ^{4}

]

Freudenburg, Gene ¹ ; Moser-Jauslin, Lucy ²

¹ University of Southern Indiana, Department of Mathematics, Evansville IN 47712 (USA)
² Université de Bourgogne, Laboratoire de Topologie, 9 avenue Alain Savary, BP 47870, 21078 Dijon Cedex (France)

Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 133-143.

Résumé
Abstract

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 $n \geq 4$ .

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.

EuDML MR Zbl

DOI : 10.5802/aif.1879

Classification : 14R20, 13A50
Keywords: nonlinearizable actions, equivariant vector bundles, invariants
Mot clés : actions non linéarisables, fibrés vectoriels équivariants, invariants

Affiliations des auteurs :

Freudenburg, Gene ¹ ; Moser-Jauslin, Lucy ²

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     title = {A nonlinearizable action of $S_3$ on ${\mathbb {C}}^4$},
     journal = {Annales de l'Institut Fourier},
     pages = {133--143},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     year = {2002},
     doi = {10.5802/aif.1879},
     mrnumber = {1881573},
     zbl = {1028.14019},
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     url = {http://www.numdam.org/articles/10.5802/aif.1879/}
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Freudenburg, Gene; Moser-Jauslin, Lucy. A nonlinearizable action of $S_3$ on ${\mathbb {C}}^4$. Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 133-143. doi : 10.5802/aif.1879. http://www.numdam.org/articles/10.5802/aif.1879/

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