Notes for AKT-091008-2/0:36:32

Claim: Given Lie-algebra [math]\displaystyle{ \mathcal{G} }[/math] and metric [math]\displaystyle{ t }[/math], we have [math]\displaystyle{ \mathcal{T}_\mathcal{G}: \mathcal{A}(|) \rightarrow U(\mathcal{G}) }[/math] s.t. given any representation [math]\displaystyle{ R }[/math], [math]\displaystyle{ \exists \ \ tr_R: U(\mathcal{G}) \rightarrow \mathbb{Q},\ \ tr_R \circ \mathcal{T}_\mathcal{G}=W_{\mathcal{G},R} }[/math].