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Moscow Mathematical Journal

Volume 15, Issue 4, Octoberโ€“December 2015  pp. 609โ€“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


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 ๐–˜๐–šp,q (p or q>1), ๐–˜๐–”p,p+2 (p odd or p=2), ๐–š*2m+1(โ„) (mโ‰ฅ1) and EIII.

2010 Math. Subj. Class. 17B20

Keywords: Lie algebra, Cartan decomposition.

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