Lie subalgebra and subspace

  • Thread starter KarateMan
  • Start date
13
0

Main Question or Discussion Point

I have a question about Lie subalgebra.

They say "a Lie subalgebra is a much more CONSTRAINED structure than a subspace".
Well, it seems subtle, and I find this very tricky to follow.

Can anyone explain this with concrete examples?

If my question is not clear, please tell me so, I will try to rephrase it.
Thanks.
 

Answers and Replies

246
1
an algebra is nececearily not a space (understood vectorspace), so there is a big different. If you are talking about an subalgebra and a lie subalgebra. I guess you know the usual deffinition of a subalgebra, a lie subalgebra is a much more strict because a lie subalgebra needs to be a algebra + a submanifold, which is very strict.
 
KarateMan: A Lie subalgebra is a linear subspace which is a Lie algebra.
Hence, besides being a subspace, it has to satisfy the Lie algebra axioms (e.g. it has to be closed under the Lie bracket!).

mrandersdk: There are no topological requirements for Lie (sub)algebras.
 
422
1
246
1
so sorry always do this, i read it as lie group, why do i always do this. Sorry again.

Neglect my comment.
 
13
0
Thanks everyone. took me a while but I think I swallowed it!
 

Related Threads for: Lie subalgebra and subspace

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
9
Views
4K
  • Last Post
Replies
8
Views
862
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
23
Views
6K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
824
  • Last Post
Replies
12
Views
2K
Top