Actions of \(G_a\) on \(\mathbb{A}^3\) defined by homogeneous derivations
type: Item
instance of: scholarly article
title: Actions of \(G_a\) on \(\mathbb{A}^3\) defined by homogeneous derivations
zbMATH Open document ID: 0904.14027
DOI: 10.1016/S0022-4049(96)00143-0
author: Gene Freudenburg
published in: Journal of Pure and Applied Algebra
publication date: 1999-01-18T00:00:00Z
review text: Let \(k\) be a field. The symbol \(\mathbb{G}_a\) denotes the additive group \((k,+)\). In the present article the author studies an action of \(\mathbb{G}_a\) on the affine \(n\)-space \(\mathbb{A}^n\). In J. Pure Appl. Algebra 105, No. 3, 267-275 (1995; Zbl 0857.14024), \textit{G. Freudenburg} defined the rank of such an action. It has the following properties: (1) \(0\leq \text{rank}\leq n\); (2) an action of \(\mathbb{G}_a\) on \(\mathbb{A}^n\) of rank \(r\) can be embedded into one of \(\mathbb{G}_a\) on \(\mathbb{A}^{n'}\) of rank \(n'-n+r\) if \(n'>n\). If \(n=2\), then the rank is at most 1. This article gives an action of \(\mathbb{G}_a\) on \(\mathbb{A}^n\) of rank \(n\) for the first time if \(n\geq 3\).
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14H37
zbMATH DE Number: 1121695
zbMATH Keywords: algebraic group
zbMATH Keywords: rank of action
Wikidata QID: Q56689590
MaRDI profile type: Publication
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full work available at URL: s0022-4049(96)00143-0
OpenAlex ID: W1482573742
description: scientific article; zbMATH DE number 1121695