Download this article
Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2640-7345 (online)
ISSN 2640-7337 (print)
Author Index
To Appear
 
Other MSP Journals
A note on commutators in compact semisimple Lie algebras

Linus Kramer
Vol. 20 (2023), No. 2-3, 317–324
DOI: 10.2140/iig.2023.20.317
Abstract

Given any two elements A,B in a compact semisimple Lie algebra, we show that there exist elements X,Y,Z such that

A = [X,Y ] andB = [X,Z].

The proof uses Cartan subalgebras and their root systems. We also review some related problems about Cartan subalgebras in compact semisimple Lie algebras.

Dedicated to Jacques Tits
Keywords
Lie algebra, commutator, Cartan subalgebra
Mathematical Subject Classification
Primary: 22E60
Milestones
Received: 23 August 2022
Revised: 21 March 2023
Accepted: 14 May 2023
Published: 13 September 2023
Authors
Linus Kramer
Mathematisches Institut
Fachbereich Mathematik und Informatik
Universität Münster
Münster
Germany
© 2023 MSP (Mathematical Sciences Publishers).