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Transactions of the American Mathematical Society

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Nonlinearizable actions of dihedral groups on affine space


Author: Kayo Masuda
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 3545-3556
MSC (2000): Primary 14R20; Secondary 14L30, 14D20
DOI: https://doi.org/10.1090/S0002-9947-03-03405-6
Published electronically: December 15, 2003
MathSciNet review: 2055746
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Abstract: Let $G$ be a reductive, non-abelian, algebraic group defined over $\mathbb{C} $. We investigate algebraic $G$-actions on the total spaces of non-trivial algebraic $G$-vector bundles over $G$-modules with great interest in the case that $G$ is a dihedral group. We construct a map classifying such actions of a dihedral group in some cases and describe the spaces of those non-linearizable actions in some examples.


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Additional Information

Kayo Masuda
Affiliation: Mathematical Science II, Himeji Institute of Technology, 2167 Shosha, Himeji 671-2201, Japan
Email: kayo@sci.himeji-tech.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-03-03405-6
Keywords: Algebraic group action, linearization problem
Received by editor(s): April 3, 2003
Published electronically: December 15, 2003
Additional Notes: Supported by Grant-in-Aid for Young Scientists, The Ministry of Education, Culture, Sports, Science and Technology, Japan
Article copyright: © Copyright 2003 American Mathematical Society

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