On the conjugacy theorem of Cartan subalgebras.
type: Item
instance of: scholarly article
title: On the conjugacy theorem of Cartan subalgebras.
zbMATH Open document ID: 1085.17005
published in: Hiroshima Mathematical Journal
publication date: 2003-03-20T00:00:00Z
review text: Consider a finite-dimensional Lie algebra over an algebraically closed field of characteristic 0. Recall that a nilpotent subgroup which equals its normalizer is called Cartan subalgebra. It is well-known that in our context all Cartan subalgebras are conjugate. The authors give a new elementary, direct proof of this theorem, which fits into the context of \textit{N.~Bourbaki}, Groupes et algèbres de Lie, Ch.~7, 8 Herman, Paris (1975; Zbl 0329.17002). They also reprove that all Borel subalgebras (maximal solvable subalgebras) are conjugate.
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 1874209
zbMATH Keywords: Cartan subalgebra
zbMATH Keywords: Borel subalgebra
zbMATH Keywords: conjugacy theorem
author: A. A. George Michael
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1151007553
OpenAlex ID: W2133280090
Wikidata QID: Q128871796
DOI: 10.32917/HMJ/1151007553
description: scientific article; zbMATH DE number 1874209