The subalgebras of the rank two symplectic Lie algebra

Andrew Douglas; Joe Repka

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arXiv · 1704.00241

The subalgebras of the rank two symplectic Lie algebra

Andrew Douglas·Joe Repka

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Abstract

The semisimple subalgebras of the rank $2$ symplectic Lie algebra $\mathfrak{sp}(4,\mathbb{C})$ are well-known, and we recently classified its Levi decomposable subalgebras. In this article, we classify the solvable subalgebras of $\mathfrak{sp}(4,\mathbb{C})$, up to inner automorphism. This completes the classification of the subalgebras of $\mathfrak{sp}(4,\mathbb{C})$. More broadly speaking, in completing the classification of the subalgebras of $\mathfrak{sp}(4,\mathbb{C})$ we have completed the classification of the subalgebras of the rank $2$ semisimple Lie algebras.

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Andrew Douglas, Joe Repka. 2017-04-02. The subalgebras of the rank two symplectic Lie algebra. https://arxiv.org/abs/1704.00241

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