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Lie Algebra Question

  1. Oct 8, 2007 #1
    I read in Knapp's book on Lie algebras that "a 2-dimensional nilpotent Lie algebra is abelian." Why is this the case? Can somebody who knows please tell me?
     
  2. jcsd
  3. Oct 9, 2007 #2

    morphism

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    How many 2-dimensional Lie algebras are there (up to isomorphism)? There are two: one's abelian and the other's not. Try proving that the nonabliean one cannot be nilpotent.
     
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