Abstract
It is still an open question whether or not there exist polynomial automorphisms of finite order of complex affine n-space which cannot be linearized, i.e., which are not conjugate to linear automorphisms. The second author gave the first examples of non-linearizable actions of positive dimensional groups, and Masuda and Petrie did the same for finite groups.
These examples were all obtained from non-trivial G-vector bundles on representation spaces using ideas of Bass and Haboush. So far, this approach has failed for commutative groups and in particular for automorphisms of finite order. The reason is given by a recent theorem due to Masuda, Moser-Jauslin and Petrie showing that for a commutative reductive group G every G-vector bundle on a representation space of G is trivial.
The aim of this report is to give an introduction to the subject, to describe some basic results and to present a short proof of the theorem of Masuda, Moser-Jauslin and Petrie from a different perspective (cf. [18]).
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Kraft, H., Schwarz, G. (1995). Finite Automorphisms of Affine N-Space. In: van den Essen, A. (eds) Automorphisms of Affine Spaces. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8555-2_3
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DOI: https://doi.org/10.1007/978-94-015-8555-2_3
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