Let L1 and L2 be two abelian Lie algebras. I need to show that L1 and L2 are isomorphic if and only if they have the same dimension.
Unfortunately I have no idea how to solve this. Can someone help?
2026-04-06 13:10:02.1775481002
abelian lie algebras of the same dimension are isomorphic
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If they don't have the same dimension, then they are not isomorphic as vector spaces and therefore they are not isomorphic as Lie algebras.
And if they have the same dimension, take any linear isomorphism between them and then, since both Lie algebras are abelian, it will automatically be a Lie algebra isomorphism.