Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 362 页 · Chapter VI，Section 3「Cartan Decomposition」，Theorem 6.31(g)
Theorem 6.31. Let $G$ be a semisimple Lie group, let $\theta$ be a Cartan involution of its Lie algebra $\mathfrak g_0$, let $\mathfrak g_0 = \mathfrak k_0 \oplus \mathfrak p_0$ be the corresponding Cartan decomposition, and let $K$ be the analytic subgroup of $G$ with Lie algebra $\mathfrak k_0$. Then [...] (g) when $Z$ is finite, $K$ is a maximal compact subgroup of $G$.