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
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
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

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

Lie algebra, commutator, Cartan subalgebra
Mathematical Subject Classification
Primary: 22E60
Received: 23 August 2022
Revised: 21 March 2023
Accepted: 14 May 2023
Published: 13 September 2023
Linus Kramer
Mathematisches Institut
Fachbereich Mathematik und Informatik
Universität Münster