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The subalgebras of the rank two symplectic Lie algebra. (English) Zbl 1419.17016
Summary: 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.

17B20 Simple, semisimple, reductive (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B30 Solvable, nilpotent (super)algebras
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