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arXiv · 1501.02934

On the commutator map for real semisimple Lie algebras

Dmitri Akhiezer
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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 $p=2$), $\mathfrak u^*_{2m+1}(\mathbb H)$ ($m\ge 1$) and $EIII$.

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Dmitri Akhiezer. 2015-01-13. On the commutator map for real semisimple Lie algebras. https://arxiv.org/abs/1501.02934

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