Notes for AKT-091006/0:11:24

Choose basis [math]\displaystyle{ (X_a) }[/math], [math]\displaystyle{ a \in \{1, 2, \cdots, \dim(\mathcal{G}) \} }[/math] for [math]\displaystyle{ \mathcal{G} }[/math] and basis [math]\displaystyle{ (e_a) }[/math], [math]\displaystyle{ a \in \{1, 2, \cdots, \dim(R) \} }[/math] for [math]\displaystyle{ R }[/math]

Notation: Let [math]\displaystyle{ [X_a, X_b] = F_{a,b}^n X_n }[/math], [math]\displaystyle{ F_{ab}^n \in \mathbb{Q} }[/math]

[math]\displaystyle{ \lt X_a, X_b\gt = t_{ab} }[/math]; [math]\displaystyle{ t^{ab} }[/math] is defined s.t. [math]\displaystyle{ t_{ab} \cdot t^{bc} = \delta_{ac} }[/math]