I was given a basis and a bracket denoting a bunch of relations on this basis of a Lie algebra. I am trying to prove that i have in fact been given a Lie algebra and thus that the bracket upholds the Jacobi identity.
The example i have is 7 dimensional thus i have a bunch of cases to check although i can eleminate a couple since i'm working with a nilpotent space. I was wondering if there is a 'smart' method to do this or if there are some sufficiant conditions, instead of going over every possible 3-tuple of basis elements.