Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 660 页 · Appendix B「Lie's Third Theorem」，Section 1「Levi Decomposition」，Theorem B.2
Theorem B.2 (Levi decomposition). If $\mathfrak g$ is a finite-dimensional Lie algebra over $\mathbb R$, then there exists a semisimple subalgebra $\mathfrak s$ of $\mathfrak g$ such that $\mathfrak g$ is the semidirect product $\mathfrak g = \mathfrak s \oplus_\pi (\operatorname{rad}\mathfrak g)$ for a suitable homomorphism $\pi\colon\mathfrak s\to\operatorname{Der}_{\mathbb R}(\operatorname{rad}\mathfrak g)$.