This article is cited in 6 papers

On the commutator map for real semisimple Lie algebras

Dmitri Akhiezer

Institute for Information Transmission Problems, 19 B. Karetny per., 127994 Moscow, Russia

Abstract: 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 $\mathfrak{su}_{p,q}$ ($p$ or $q>1$), $\mathfrak{so}_{p,p+2}$ ($p$ odd or $p=2$), $\mathfrak u^*_{2m+1}(\mathbb H)$ ($m\ge1$) and $EIII$.

Key words and phrases: Lie algebra, Cartan decomposition.

MSC: 17B20

Received: January 14, 2015; in revised form June 7, 2015

Language: English

DOI: 10.17323/1609-4514-2015-15-4-609-613

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