The subalgebras of $\mathfrak{so}(4,\mathbb{C})$
Abstract: We classify the solvable subalgebras, semisimple subalgebras, and Levi decomposable subalgebras of $\mathfrak{so}(4,\mathbb{C})$, up to inner automorphism. By Levi's Theorem, this is a full classification of the subalgebras of $\mathfrak{so}(4,\mathbb{C})$.
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