Automorphisms of semisimple real Lie algebras
type: Item
instance of: scholarly article
title: Automorphisms of semisimple real Lie algebras
zbMATH Open document ID: 0707.17011
DOI: 10.1007/BF01078795
author: Yu. G. Khatskevich
publication date: 1989-01-01T00:00:00Z
review text: Consider a simple complex Lie algebra \({\mathfrak g}^ c\) with real form \({\mathfrak g}\). Let \(Aut_ e{\mathfrak g}^ c\) be the group of all automorphisms of \({\mathfrak g}^ c\) generated by the elements of the form exp ad x with nilpotent ad x. Let \(Aut_ 0{\mathfrak g}\) be the inverse image of \(Aut_ e{\mathfrak g}^ c\) with respect to the map Aut \({\mathfrak g}\to Aut {\mathfrak g}^ c\), \(g\mapsto g\otimes 1\), and \(Aut_ 0({\mathfrak g},{\mathfrak h})\) be the subgroup of \(Aut_ 0{\mathfrak g}\) preserving the Cartan subalgebra \({\mathfrak h}\subset {\mathfrak g}\). The author deduces a necessary and sufficient condition for certain pairs of \(Aut_ 0({\mathfrak g},{\mathfrak h})\) to be conjugate.
Mathematics Subject Classification ID: 17B40
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 4160977
zbMATH Keywords: quasi-inner automorphisms
zbMATH Keywords: conjugacy classes
MaRDI profile type: Publication
cites work: Q5662607
cites work: Q4930353
cites work: Les sous-algèbres de Cartan réelles et la frontière d'une orbite ouverte dans une variété de drapeaux
published in: Functional Analysis and Its Applications
reviewed by: Ivan Kolář
description: scientific article; zbMATH DE number 4160977