A nonlinearizable action of S 3 on 4
[Une action non linéarisable de S 3 sur 4 ]
Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 133-143.

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 n pour tout entier n4.

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.

DOI : 10.5802/aif.1879
Classification : 14R20, 13A50
Keywords: nonlinearizable actions, equivariant vector bundles, invariants
Mot clés : actions non linéarisables, fibrés vectoriels équivariants, invariants
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)
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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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