# Lie subalgebra and subspace

by KarateMan
Tags: subalgebra, subspace
 P: 13 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.
 P: 230 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.
 P: 5 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.
P: 444

## Lie subalgebra and subspace

 Quote by mrandersdk an algebra is nececearily not a space
This is terribly, terribly wrong.
 P: 230 so sorry always do this, i read it as lie group, why do i always do this. Sorry again. Neglect my comment.
 P: 13 Thanks everyone. took me a while but I think I swallowed it!

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