Global degree bounds and the transfer principle for invariants
type: Item
instance of: scholarly article
title: Global degree bounds and the transfer principle for invariants
zbMATH Open document ID: 1085.13001
author: Roger M. Bryant
author: Gregor Kemper
published in: Journal of Algebra
publication date: 2005-02-22T00:00:00Z
review text: For a linear algebraic group \(G\) over an algebraically closed field \(K\) the following are equivalent: (a) \(G\) has global degree bound on invariants (that is, there is a natural number \(d\) such that the ring of invariants is generated in degree \(\leq d\) for all algebraic \(G\)-modules); (b) \(G\) is finite with \(| G| \) invertible in \(K\). That (b) implies (a) was known before, and now the authors prove the reverse implication. This verifies a conjecture of \textit{H. Derksen} and \textit{G. Kemper} [in: Invariant theory in all characteristics, Proc. Workshop Invariant Theory, CRM Proc. Lect. Notes 35, 37--41 (2004; Zbl 1072.14056)], where the characteristic zero case was handled. Along the way the ``transfer principle'' of invariant theory is proved in a more general setting than usual.
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 16W22
zbMATH DE Number: 2136964
zbMATH Keywords: degree bound for invariants
zbMATH Keywords: transfer principle
zbMATH Keywords: linear algebraic group
reviewed by: Matyas Domokos
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.09.027
OpenAlex ID: W2105323288
cites work: Q3999894
cites work: Q4659154
cites work: Q4317713
cites work: On Weitzenbock's Theorem in Positive Characteristic
cites work: The Noether bound in invariant theory of finite groups
cites work: On Noether's bound for polynomial invariants of a finite group
cites work: Algebraic homogeneous spaces and invariant theory
cites work: Q4744461
cites work: Invariants of finite groups over fields of characteristic \(p\)
cites work: Q3975991
cites work: On a theorem of Weitzenböck in invariant theory
cites work: An elementary proof of the Weitzenböck Theorem
DOI: 10.1016/J.JALGEBRA.2004.09.027
description: scientific article; zbMATH DE number 2136964