Notes for AKT-091006/0:03:35: Difference between revisions
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Example: Let the Lie-algebra be <math>gl_n(k)</math> (with <math>[ \cdot, \cdot]</math> being the commutator and <math>< A, B>= tr(AB)</math>) |
Example: Let the Lie-algebra be <math>gl_n(k)</math> (with <math>[ \cdot, \cdot]</math> being the commutator and <math>< A, B>= tr(AB)</math>) |
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Let the representation <math>R</math>: <math>\rho: \mathcal{G} \rightarrow End |
Let the representation <math>R</math>: <math>\rho: \mathcal{G} \rightarrow End(R), \rho([A, B]) = \rho(A) \circ \rho(B) - \rho(B) \circ \rho(A)</math> |
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Revision as of 00:21, 10 October 2009
Example: Let the Lie-algebra be (with being the commutator and )
![{\displaystyle [\cdot ,\cdot ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/28dd4c22d60192519c1c12cf645b040f368db9e9)
Let the representation :
![{\displaystyle \rho :{\mathcal {G}}\rightarrow End(R),\rho ([A,B])=\rho (A)\circ \rho (B)-\rho (B)\circ \rho (A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7225dccb450e84217be844f377019c90b3847da2)
