The deformation of Lie algebra ?

[Esmaeil]

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)?

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[Incnis Mrsi]

What’s the question? From the perspective of tensor calculus, the structure of a Lie algebra is (1,2) tensor C^k_ij 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.