Actions of compact Lie groups on homogeneous spaces
type: Item
instance of: scholarly article
title: Actions of compact Lie groups on homogeneous spaces
zbMATH Open document ID: 0546.57017
DOI: 10.1007/BF01168154
author: Volker Hauschild
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173595
review text: Let G be a compact simple Lie group acting on the homogeneous space \(X=G/T\) (T a maximal torus) with finitely many orbit types. Then it is shown that G acts always in the natural way up to conjugation. This follows in particular from the fact that a graded homomorphism \(H^*(G/T;{\mathbb{R}})\to H^*(G/T;{\mathbb{R}})\) is either trivial or an isomorphism in connection with classical results in the cohomology theory of transformation groups.
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 57T15
Mathematics Subject Classification ID: 55N91
zbMATH DE Number: 3870244
zbMATH Keywords: reflection groups
zbMATH Keywords: flag manifolds
zbMATH Keywords: endomorphisms of cohomology rings
zbMATH Keywords: actions on compact homogeneous spaces
zbMATH Keywords: compact simple Lie group
zbMATH Keywords: cohomology theory of transformation groups
Wikidata QID: Q115393972
MaRDI profile type: Publication
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OpenAlex ID: W2090072031
description: scientific article; zbMATH DE number 3870244