Talk:Lie groups I: Definition and examples

From Manifold Atlas
Revision as of 09:35, 9 June 2010 by Kuessner (Talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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.

Personal tools
Namespaces
Variants
Actions
Navigation
Interaction
Toolbox