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The deformation of Lie algebra ?

  1. Aug 16, 2014 #1
    How can we deform a given Lie algebra? In particular, in the attachment file how can we arrive at the commutation relations (20) by starting from the commutation relation (19)?
  2. jcsd
  3. Aug 28, 2014 #2
    I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
  4. Sep 3, 2014 #3
    What’s the question? From the perspective of tensor calculus, the structure of a Lie algebra is (1,2) tensor Ckij antisymmetric under i, j and satisfying a quadratic equation known as the Jacobi identity. The equation has very special form, so it not only has other solutions, but, as authors claim, even 1-parametric analytic families of solutions (it’s this that is usually called a deformation). Some solutions may be equivalent (up to linear transformations) to the original algebra, whereas others are not.
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