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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.

MSC:
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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References:
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