A nonlinearizable action of S 3 on ℂ 4

Gene Freudenburg[1]; Lucy Moser-Jauslin[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 (2002)

  • Volume: 52, Issue: 1, page 133-143
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Freudenburg, Gene, and Moser-Jauslin, Lucy. "A nonlinearizable action of $S_3$ on ${\mathbb {C}}^4$." Annales de l’institut Fourier 52.1 (2002): 133-143. <http://eudml.org/doc/115969>.

@article{Freudenburg2002,
abstract = {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.},
affiliation = {University of Southern Indiana, Department of Mathematics, Evansville IN 47712 (USA); Université de Bourgogne, Laboratoire de Topologie, 9 avenue Alain Savary, BP 47870, 21078 Dijon Cedex (France)},
author = {Freudenburg, Gene, Moser-Jauslin, Lucy},
journal = {Annales de l’institut Fourier},
keywords = {nonlinearizable actions; equivariant vector bundles; invariants; linearization problem; group actions},
language = {eng},
number = {1},
pages = {133-143},
publisher = {Association des Annales de l'Institut Fourier},
title = {A nonlinearizable action of $S_3$ on $\{\mathbb \{C\}\}^4$},
url = {http://eudml.org/doc/115969},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Freudenburg, Gene
AU - Moser-Jauslin, Lucy
TI - A nonlinearizable action of $S_3$ on ${\mathbb {C}}^4$
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 1
SP - 133
EP - 143
AB - 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.
LA - eng
KW - nonlinearizable actions; equivariant vector bundles; invariants; linearization problem; group actions
UR - http://eudml.org/doc/115969
ER -

References

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  11. M. Masuda, L. Moser-Jauslin, T. Petrie, The equivariant Serre problem for abelian groups, Topology 35 (1996), 329-334 Zbl0884.14007MR1380501
  12. K. Mederer, Moduli of G -equivariant vector bundles, (1995) 
  13. L. Moser-Jauslin, Triviality of certain equivariant vector bundles for finite cyclic groups, C.R. Acad. Sci. Paris 317 (1993), 139-144 Zbl0813.14033MR1231410
  14. D. Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167-171 Zbl0337.13011MR427303
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