# Math Help - who can proof the lie's theorem?

1. ## who can proof the lie's theorem?

Let V be an n-dimensional complex vector space and let L be a solveable Lie algebra of gl(V) . Then there is a basis of V in which every element of L is represented by an upper triangular matrix.

2. ## Re: who can proof the lie's theorem?

Originally Posted by vernal
Let V be an n-dimensional complex vector space and let L be a solveable Lie algebra of gl(V) . Then there is a basis of V in which every element of L is represented by an upper triangular matrix.
This is not too hard depending upon what you know, are you aware of Dynkin's lemma? Moreover, have you checked the standard references (e.g. Humphreys or Fulton/Harris) it's in almost all of them.

3. ## Re: who can proof the lie's theorem?

Originally Posted by vernal
who can proof the lie's theorem?
One of them: Lie.

4. ## Re: who can proof the lie's theorem?

Originally Posted by Drexel28
This is not too hard depending upon what you know, are you aware of Dynkin's lemma? Moreover, have you checked the standard references (e.g. Humphreys or Fulton/Harris) it's in almost all of them.
thanks. I find it.