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 , for and basis , for
Notation: Let ,
![{\displaystyle [X_{a},X_{b}]=F_{a,b}^{n}X_{n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/48876a09c495ff70f7cf818fed5bd205ce716a37)
; is defined s.t.
