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Lie algebra

  1. Aug 7, 2011 #1
    hi friends !!
    it is well known that a Lie algebra over K is a K-vector space g equipped
    of a K-bilinear, called Lie bracket. I ask how can we determines the Lie algebra of any vector space then? For example we try the Lie algebra of horizontal space.
  2. jcsd
  3. Aug 7, 2011 #2


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    You seem to have the idea that there is such a thing as "the" Lie Algebra of a vector space. That's not true. There exist an infinite number of Lie Algebras for a given vector space.
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