Uniqueness questions in real algebraic transformation groups
type: Item
instance of: scholarly article
title: Uniqueness questions in real algebraic transformation groups
zbMATH Open document ID: 1054.14075
DOI: 10.1016/S0166-8641(01)00067-0
author: Karl Heinz Dovermann
author: Mikiya Masuda
published in: Topology and its Applications
publication date: 2002-05-27T00:00:00Z
review text: Let \(G\) be a compact Lie group and \(H\) a closed subgroup. The authors show that the homogeneous space \(G/H\) has a unique structure as a real algebraic \(G\)-variety. For a real algebraic \(G\)-variety they show that the balanced product \(G\times_H X\) has the structure of a real algebraic \(G\)-variety, and this structure is uniquely determined by the structure on \(X\). On the other hand, suppose that \(M\) is a closed smooth \(G\)-manifold with positive dimensional orbit space \(M/G\). If \(M\) has a \(G\)-equivariant real algebraic model, then it has an uncountable family of birationally inequivariant such models.
reviewed by: Mina Teicher
Mathematics Subject Classification ID: 14P25
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 1746064
zbMATH Keywords: homogeneous space
zbMATH Keywords: real algebraic model
MaRDI profile type: Publication
cites work: Q5563439
cites work: Orbits of linear algebraic groups
cites work: Q3770650
cites work: Nonisomorphic algebraic models of a smooth manifold
cites work: Q3999894
cites work: Arithmetic subgroups of algebraic groups
cites work: Q5658847
cites work: Q3704110
cites work: Q5842420
cites work: Algebraic realization of manifolds with group actions
cites work: Q4281980
cites work: Nonisomorphic Algebraic Models of a Smooth Manifold with Group Action
cites work: Q4143433
cites work: Q5339349
cites work: Q4089001
cites work: Q3993222
cites work: Espaces Homogènes De Stein Des Groupes De Lie Complexes
cites work: Q3998356
cites work: Q4391371
cites work: Inequalities defining orbit spaces
cites work: Smooth functions invariant under the action of a compact Lie group
cites work: Q3490128
cites work: Quotients of real algebraic \(G\) varieties and algebraic realization problems
cites work: Extending algebraic actions
cites work: Elementary structure of real algebraic varieties
full work available at URL: s0166-8641(01)00067-0
OpenAlex ID: W2007051885
description: scientific article; zbMATH DE number 1746064