Complexification of a Lie algebra
= Complexification of a Lie algebra
For a real Lie algebra $\mathfrak g$, its complexification is $\mathfrak g_{\mathbb C}=\mathfrak g\otimes_{\mathbb R}\mathbb C$ with the bracket extended complex-bilinearly.
= Complexification of a Lie algebra
For a real Lie algebra $\mathfrak g$, its complexification is $\mathfrak g_{\mathbb C}=\mathfrak g\otimes_{\mathbb R}\mathbb C$ with the bracket extended complex-bilinearly.