
#1
Mar1208, 01:39 AM

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. 



#2
Mar1208, 07:44 AM

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.




#3
Mar1208, 12:51 PM

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. 



#4
Mar1208, 01:34 PM

P: 448

Lie subalgebra and subspace 



#5
Mar1308, 02:02 AM

P: 230

so sorry always do this, i read it as lie group, why do i always do this. Sorry again.
Neglect my comment. 



#6
Mar1608, 09:53 PM

P: 13

Thanks everyone. took me a while but I think I swallowed it!



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