Lie algebra

  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. HallsofIvy

    HallsofIvy 40,241
    Staff Emeritus
    Science Advisor

    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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