A note on homogeneous Kähler manifolds of semi-simple Lie groups
type: Item
instance of: scholarly article
title: A note on homogeneous Kähler manifolds of semi-simple Lie groups
zbMATH Open document ID: 0829.53045
author: Yūta Hayashi
author: Kazufumi Nakajima
published in: Journal of Mathematics of Kyoto University
publication date: 1996-01-17T00:00:00Z
review text: In this short note the author proves the following Theorem. Let \(G/K\) be a homogeneous Kähler manifold of a semi-simple Lie group \(G\). Then \(\text{Aut} (G/K)\) is semi-simple. Assume further that \(G\) acts effectively on \(G/K\) and that every simple factor of \(G\) is of non- compact type. Then \(G\) coincides with \(\text{Aut} (G/K)_0\). Here \(\text{Aut}(G/K)\) denotes the group of all holomorphic isometries of \(G/K\) and \(\text{Aut} (G/K)_0\) its identity component. The theorem is generalising the well-known fact that for a Hermitian symmetric space of non-compact type \(G/K\), \(G\) coincides with \(\text{Aut}(G/K)_0\) under the effectiveness assumption on \(G\).
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32M10
zbMATH DE Number: 775697
zbMATH Keywords: automorphism group
zbMATH Keywords: holomorphic isometric
zbMATH Keywords: homogeneous Kähler manifold
zbMATH Keywords: semi-simple Lie group
Wikidata QID: Q115240422
reviewed by: Novica Blažić
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518883
OpenAlex ID: W1482587345
DOI: 10.1215/KJM/1250518883
description: scientific article; zbMATH DE number 775697