On normal subgroups of semisimple Lie groups
type: Item
instance of: scholarly article
title: On normal subgroups of semisimple Lie groups
zbMATH Open document ID: 1202.22010
published in: Results in Mathematics
publication date: 2010-10-14T00:00:00Z
review text: The article is devoted to prove the following result: Every normal subgroup of a finite-di\-men\-sion\-al real semisimple Lie group is closed in the topology of the Lie group. This is a generalization of the result by \textit{D. L. Ragozin} [Proc. Am. Math. Soc. 32, 632--633 (1972; Zbl 0231.22012)]. Whereas Ragozin imposed the hypothesis of being connected for semisimple Lie groups, the present article gives a proof removing this assumption. The proof is done by induction on the dimension of the Lie group and uses essentially the notions and properties of arc component and centre of a group.
reviewed by: Angel Francisco Tenorio Villalon
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 5800212
zbMATH Keywords: normal subgroup
zbMATH Keywords: semisimple Lie groups
zbMATH Keywords: closed sets
zbMATH Keywords: semisimple Lie algebras
author: A. A. George Michael
MaRDI profile type: Publication
full work available at URL: s00025-010-0038-0
OpenAlex ID: W2142222292
Wikidata QID: Q115389903
cites work: Q3994903
cites work: Shorter Notes: A Normal Subgroup of a Semisimple Lie Group is Closed
DOI: 10.1007/S00025-010-0038-0
description: scientific article; zbMATH DE number 5800212