Talk:Lie groups I: Definition and examples

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(Created page with 'Theorem 2.2 is wrong as stated. A counterexample is given on page 83 of {{cite|Carter&Segal&Macdonald1995}}. For each Lie group one has the adjoint representation $Ad:G\rightarr…')
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Revision as of 10:35, 9 June 2010

Theorem 2.2 is wrong as stated. A counterexample is given on page 83 of [Carter&Segal&Macdonald1995].

For each Lie group one has the adjoint representation $Ad:G\rightarrow GL\left(g\right)$. This representation is faithful if $G$ is semisimple. Thus Theorem 2.2 is correct for semisimple Lie groups.

I'm going to add the condition "G semisimple" to the assumptions of Theorem 2.2.