0

I do not understand the topology of a Lie group clearly. Let $G$ be a Lie group and $T_eG$ be its tangent space at the identity $e \in G$. Why $Aut(T_eG)$ is an open subset of the vector space of endomorphisms of $T_eG$ (i.e. $End(T_eG)$)? What does "open" mean?

flag
6 
 This question is not really at an appropriate level for this site. You should try math.stackexchange.com which is a better forum for asking undergraduate level questions like "what is the usual topology on a vector space." – Noah Snyder Jan 2 2011 at 4:08
1 
 If you are working with finite-dimensional Lie groups, then the tangent space at the identity is a finite-dimensional vector space, so endormorphisms of it form a finite-dimensional vector space, which has a canonical topology. If you are looking at infinite-dimensional Lie groups (e.g. Frechet Lie groups) then there are perhaps some problems, because the exponential map $T_eG \to G$ ceases to become surjective on an open neighbourhood of the identity. – David Roberts Jan 2 2011 at 4:16
And I echo Noah's sentiments. Try math.stackexchange.com if what I said is not enough. – David Roberts Jan 2 2011 at 4:17
Thank you very much. – Jianrong Li Jan 2 2011 at 4:19

closed as too localized by Noah Snyder, Andres Caicedo, Andy Putman, Deane Yang, S. Carnahan♦ Jan 2 2011 at 4:35

Browse other questions tagged or ask your own question.