Universal transitivity of simple and 2-simple prehomogeneous vector spaces
type: Item
instance of: scholarly article
title: Universal transitivity of simple and 2-simple prehomogeneous vector spaces
zbMATH Open document ID: 0606.14037
author: B. George
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74797
review text: We denote by k a field of characteristic zero satisfying \(H^ 1(k,Aut(SL_ 2))\neq 0\). Let G be a connected k-split linear algebraic group acting on \(X=Aff^ n\) rationally by \(\rho\) with a Zariski-dense G- orbit Y. A prehomogeneous vector space (G,\(\rho\),X) is called ''universally transitive'' if the set of k-rational points Y(k) is a single \(\rho\) (G)(k)-orbit for all such k. Such prehomogeneous vector spaces are classified by J. Igusa when \(\rho\) is irreducible. We classify them when G is reductive and its commutator subgroup [G,G] is either a simple algebraic group or a product of two simple algebraic groups.
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 12G05
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 3979256
zbMATH Keywords: prehomogeneous vector spaces
zbMATH Keywords: Galois cohomology
MaRDI profile type: Publication
OpenAlex ID: W2328123087
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DOI: 10.5802/AIF.1133
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 3979256