Algorithmic invariant theory of nonreductive groups
type: Item
instance of: scholarly article
title: Algorithmic invariant theory of nonreductive groups
zbMATH Open document ID: 1262.14055
author: Tobias Kamke
author: Gregor Kemper
published in: Qualitative Theory of Dynamical Systems
publication date: 2013-02-05T00:00:00Z
review text: Let \(X\) be an affine variety over the algebraically closed field \(K\) and \(G\) a linear algebraic group over \(K\) acting on \(X\). The paper gives a survey of algorithms in invariant theory with an emphasis on nonreductive groups. A new method for computing the ring of invariants \(K[X]^G\) is presented. It is assumed that the invariant field \(K(X)^G\) is equal to the field of fractions of \(K[X]^G\). This is satisfied for unipotent groups. There is also a new result on separating invariants. There exists a separating set of invariants of size and most \(2\cdot\dim(K[X]^G)+1\). Here a subset \(S\subseteq K[X]^G\) is called separating, if the following condition holds for all points \(p, q\in X:\) If there exists \(f\in K[X]^G\) with \(f(p)\neq f(q)\), then there exists \(g\in S\) with \(g(p)\neq g(q)\).
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 13P99
zbMATH DE Number: 6134567
zbMATH Keywords: Invariant theory
zbMATH Keywords: nonreductive groups
zbMATH Keywords: algorithms
describes a project that uses: Maple
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: s12346-011-0059-4
OpenAlex ID: W2079904820
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DOI: 10.1007/S12346-011-0059-4
description: scientific article; zbMATH DE number 6134567