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

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