Notes for AKT-091013/0:03:17

Facts about $U({\mathcal {G}})$:

1. $U({\mathcal {G}})$ is an (non-communicative) algebra

2. $U({\mathcal {G}})$ is a co-algebra

3. $U({\mathcal {G}}_{1}\oplus {\mathcal {G}}_{2})\cong U({\mathcal {G}}_{1})\otimes U({\mathcal {G}}_{2})$

4. $U({\mathcal {G}})\cong S({\mathcal {G}})$ as co-algebras and ${\mathcal {G}}$ modules