The subalgebras of $\mathfrak{so}(4,\mathbb{C})$

TL;DR

This paper provides a comprehensive classification of all subalgebras of the complex Lie algebra rak{so}(4,b C), including solvable, semisimple, and Levi decomposable types, up to inner automorphism.

Contribution

It offers the first complete classification of all subalgebras of rak{so}(4,b C), utilizing Levi's Theorem to cover all cases.

Findings

Classification of solvable subalgebras

Classification of semisimple subalgebras

Classification of Levi decomposable subalgebras

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 $\mathfrak{so}(4,\mathbb{C})$.