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Homework Help: Derived lie algebra

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the derived lie algebra of [itex]\mathfrak{so}_3 \mathbb{C}[/itex], the 3x3 antisymmetric matrices with entries in [itex]\mathbb{C}[/itex] with Lie bracket the matrix commutator [itex][X,Y]=XY-YX[/itex] for any [itex]X,Y\in \mathfrak{so}_3 \mathbb{C}[/itex].

    3. The attempt at a solution

    Since [itex]\mathfrak{so}_3 \mathbb{C}[/itex] is simple the derived lie algebra of [itex]\mathfrak{so}_3 \mathbb{C}[/itex] (an ideal) must equal [itex]\mathfrak{so}_3 \mathbb{C}[/itex]. Is this right? If so, how do I justify this?
    Last edited: Sep 23, 2011
  2. jcsd
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