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Homework Help: Mapping between Lie algebras

  1. Sep 29, 2011 #1
    If a mapping between Lie algebras [itex]\varphi : \mathfrak{g} \to \mathfrak{h}[/itex] takes a basis in [itex]\mathfrak{g}[/itex] to a basis in [itex]\mathfrak{h}[/itex] is it an isomorphism of vector spaces?
     
  2. jcsd
  3. Sep 29, 2011 #2

    Office_Shredder

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    Re: Mapping

    Good question. What do you think?
     
  4. Sep 30, 2011 #3
    Re: Mapping

    I'm fairly sure it is. Is that right?
     
  5. Sep 30, 2011 #4

    HallsofIvy

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    Re: Mapping

    Assuming that by "takes a basis to a basis" you mean "one to one and onto", a Lie Algebra is completely determined by its basis, isn't it?
     
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