Centralizers of locally nilpotent derivations
type: Item
instance of: scholarly article
title: Centralizers of locally nilpotent derivations
zbMATH Open document ID: 0890.14027
DOI: 10.1016/S0022-4049(96)00064-3
author: David R. Finston
author: S Walcher
published in: Journal of Pure and Applied Algebra
publication date: 1998-06-25T00:00:00Z
review text: A \(G_a\)-action on the polynomial ring \(\mathbb C[x_1, \ldots, x_n]\) is called triangulable in case there is a coordinate system \(\{u_1, \ldots, u_n\}\) such that the group action has the form \(\sigma_t(u_1) = u_1, \sigma_t(u_i) = u_i + Q_i\) with \(Q_i \in \mathbb C[u_1, \ldots, u_{i-1}]\) for \(i > 1.\) One consequence of the Jung-van der Kulk theorem is that all \(G_a\)-actions on \(\mathbb C [x_1,x_2]\) are triangulable. Moreover algebraic actions of the additive group \(G_a\) on \(\mathbb C[x_1, \ldots, x_n]\), locally nilpotent derivations of \(\mathbb C[x_1, \ldots, x_n],\) and vector fields on \(\mathbb C^n\) admitting a strictly polynomial flow, are equivalent objects. The authors investigate the polynomial centralizer of the vector field corresponding to a triangulable locally nilpotent derivation. In particular this yields a criterion for triangulability. This allows to present several new examples of nontriangulable \(G_a\)-actions extending those previously known in the literature.
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14E07
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 13N05
zbMATH DE Number: 1061804
zbMATH Keywords: \(G_ a\)-action
zbMATH Keywords: locally nilpotent derivation
zbMATH Keywords: triangulable action
zbMATH Keywords: polynomial flow
reviewed by: Peter Schenzel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1061804