Notes for AKT-091013/0:03:17
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Facts about [math]\displaystyle{ U(\mathcal{G}) }[/math]:
1. [math]\displaystyle{ U(\mathcal{G}) }[/math] is an (non-communicative) algebra
2. [math]\displaystyle{ U(\mathcal{G}) }[/math] is a co-algebra
3. [math]\displaystyle{ U(\mathcal{G}_1 \oplus \mathcal{G}_2) \cong U(\mathcal{G}_1) \otimes U(\mathcal{G}_2) }[/math]
4. [math]\displaystyle{ U(\mathcal{G}) \cong S(\mathcal{G}) }[/math] as co-algebras and [math]\displaystyle{ \mathcal{G} }[/math] modules
