Locally smooth \(\text{SU}(n+1)\)-actions on \(\text{SU}(n+1)/\text{S}(\text{U}(n-1) \times \text{U}(2))\) are unique
type: Item
instance of: scholarly article
title: Locally smooth \(\text{SU}(n+1)\)-actions on \(\text{SU}(n+1)/\text{S}(\text{U}(n-1) \times \text{U}(2))\) are unique
zbMATH Open document ID: 1107.22013
author: Volker Hauschild
published in: Transformation Groups
publication date: 2007-01-24T00:00:00Z
review text: Let \(G\) be a compact connected Lie group and let \(U\subset G\) be a closed connected subgroup. The homogeneous space \(G/U\) is called \textit{standard} if every locally smooth effective action of \(G\) on \(G/U\) is conjugate to the action given by left translation. The author proves that \(\text{SU}(n+1)/\text{S}(\text{U}(n-1) \times \text{U}(2))\) is standard. The key of the proof is the non existence of a set of fixed points for actions of \(\text{SU}(n+1)\). This can be done through the study of equivariant cohomology for actions with principal isotropy group of positive dimension.
Mathematics Subject Classification ID: 22F30
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57T15
zbMATH DE Number: 5118031
zbMATH Keywords: \(\text{SU}(n+1)\)-actions
zbMATH Keywords: standard action
zbMATH Keywords: equivariant cohomology of homogeneous spaces
reviewed by: Gabriela Paola Ovando
MaRDI profile type: Publication
full work available at URL: s00031-005-1105-6
OpenAlex ID: W1979769294
DOI: 10.1007/S00031-005-1105-6
description: scientific article; zbMATH DE number 5118031