Isomorphism Invariants of Restricted Enveloping Algebras

Let L and H be finite-dimensional restricted Lie algebras over a perfect field F such that u(L) = u(H), where u(L) is the restricted enveloping algebra of L. We prove that if L is p-nilpotent and abelian, then L = H . We deduce that if L is abelian and F is algebraically closed, then L = H . We use these results to prove the main result of this paper stating that if L is p-nilpotent, then L/L + γ3(L) = H/H ′p + γ3(H).