On automorphisms and adjoint orbits of real semisimple Lie algebras
type: Item
instance of: scholarly article
title: On automorphisms and adjoint orbits of real semisimple Lie algebras
zbMATH Open document ID: 0594.17011
DOI: 10.1016/0021-8693(85)90202-9
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: If \(G\) is the automorphism group and \(G_0\) the adjoint group of a real semisimple Lie algebra \({\mathfrak g}\), then there exists \(a\in G\) such that \(a(x)\in -G_0\cdot x\), for all \(x\in {\mathfrak g}\). The set of all \(a\) having this property is shown to be the same connected component \(G^*\) of \(G\), characterized differently by D. Vogan [see \textit{A. Borel} and \textit{N. Wallach}, ''Continuous cohomology, discrete subgroups, and representations of reductive groups'', Ann. Math. Stud. 94 (page 40) (1980; Zbl 0443.22010)]. The remainder of the paper is concerned with the problem of identifying \(G^*\) and with giving some information about the centralizer in \(G\) of a subalgebra \({\mathfrak s}\in {\mathfrak {sl}}(2,{\mathbb{R}})\) of \({\mathfrak g}\).
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 3955167
zbMATH Keywords: automorphism group
zbMATH Keywords: adjoint group
zbMATH Keywords: real semisimple Lie algebra
zbMATH Keywords: connected component
Wikidata QID: Q115366915
author: Dragomir Ž. Đoković
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90202-9
OpenAlex ID: W2020377036
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description: scientific article; zbMATH DE number 3955167