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

  1. #1
    Member vernal's Avatar
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    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.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: who can proof the lie's theorem?

    Quote Originally Posted by vernal View Post
    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.
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    MHF Contributor FernandoRevilla's Avatar
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    Re: who can proof the lie's theorem?

    Quote Originally Posted by vernal View Post
    who can proof the lie's theorem?
    One of them: Lie.
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  4. #4
    Member vernal's Avatar
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    Re: who can proof the lie's theorem?

    Quote Originally Posted by Drexel28 View Post
    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.
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