- Thread starter
- #1
ModusPonens
Well-known member
- Jun 26, 2012
- 45
Hello
I'm looking for tips (and just tips) on how to prove the proposition in the title: If a Lie group is abelian, its Lie algebra has Lie bracket = zero. I know I have to prove that the Lie bracket of the left invariant vector fields (to which the Lie algebra is isomorphic) is zero. But that is as far as I can get. I can't find a way to relate the commutativity of the Lie group with the Lie bracket.
Thanks in advance.
I'm looking for tips (and just tips) on how to prove the proposition in the title: If a Lie group is abelian, its Lie algebra has Lie bracket = zero. I know I have to prove that the Lie bracket of the left invariant vector fields (to which the Lie algebra is isomorphic) is zero. But that is as far as I can get. I can't find a way to relate the commutativity of the Lie group with the Lie bracket.

Thanks in advance.