Moscow Mathematical Journal

Volume 15, Issue 4, October–December 2015 pp. 609–613.

On the Commutator Map for Real Semisimple Lie Algebras

Authors: Dmitri Akhiezer
Author institution:Institute for Information Transmission Problems, 19 B. Karetny per., 127994 Moscow, Russia

Summary:

We find new sufficient conditions for the commutator map of a real semisimple Lie algebra to be surjective. As an application, we prove the surjectivity of the commutator map for all simple algebras except 𝖘𝖚_p,q (p or q>1), 𝖘𝖔_p,p+2 (p odd or p=2), 𝖚^*_2m+1(ℍ) (m≥1) and EIII.

2010 Math. Subj. Class. 17B20

Keywords: Lie algebra, Cartan decomposition.

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