Linearizing some ℤ/2ℤ actions on affine space

Jerzy Jurkiewicz
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Jerzy Jurkiewicz: University of Warsaw, Institute of Mathematics

A chapter in Algebraic Geometry, 1990, pp 243-245 from Springer

Abstract: Abstract Let V be the affine space k n over an algebraically closed field k, G a linearly reductive group and A: G×V → V a group action with a fixed point, say the origin. Then for all g ∈ G let me denote by A(g) the corresponding automorphism of V. We have $$A(g) = L(g) + D(g)$$ where L(g), D(g)∈ End V, L(g) linear and D(g) the sum of terms of higher degrees. Let me recall the well known linearization problem: is the action A linearizable, i.e. conjugated to the linear action L: G ×V →V (see e.g. [B] and [K])? Recently counter-examples have been found, see [S] and [K + S], so it is reasonable to study additional assumptions on the action A. One of them is considered in the present paper.

Keywords: Contemporary Mathematic; Reductive Group; Affine Space; Linear Action; Linear Endomorphism (search for similar items in EconPapers)
Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0685-3_11

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DOI: 10.1007/978-94-009-0685-3_11

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