The deformation of Lie algebra ?

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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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