Notes for AKT-091006/0:11:24: Difference between revisions
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and basis <math>(e_a)</math>, <math>a \in \{1, 2, \cdots, \dim(R) \}</math> for <math>R</math> |
and basis <math>(e_a)</math>, <math>a \in \{1, 2, \cdots, \dim(R) \}</math> for <math>R</math> |
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Notation: Let <math>[X_a, X_b] = F_{a,b}^n X_n</math>, <math>F_{ab}^n \in \mathbb{Q}</math> |
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express all Lie-algebra operations in terms of the basis. |
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<math><X_a, X_b> = t_{ab}</math>; <math>t^{ab}</math> is defined s.t. <math>t_{ab} \cdot t^{bc} = \delta_{ac}</math> |
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Revision as of 01:05, 10 October 2009
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]
