Notes for AKT-091001-2/0:13:25

Theorem:

1) Given a metrized, finite-dimensional Lie algebra [math]\displaystyle{ \mathcal{G} }[/math] and a finite-dimensional representation [math]\displaystyle{ R }[/math] of [math]\displaystyle{ \mathcal{G} }[/math], [math]\displaystyle{ \exists }[/math] (an interesting) linear functional [math]\displaystyle{ W_{\mathcal{G},R}: \mathcal{A} \rightarrow \mathbb{Q} }[/math] (the ground field on which [math]\displaystyle{ \mathcal{G} }[/math] is defined).