A question: Lie algebras verify Jacobi identity:
[[a,b],c] + [[b,c],a] + [[c,a],b] = 0
This is another identity with four summands:
[[[a,b],c],d] + [[[b,c],d],a] + [[[c,d],a],b] + [[[d,a],b],c] = 0
I don't know the name. I have checked that some Lie algebras verify it. I have also...