Isomorphism invariants of restricted enveloping algebras

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Let L and H be finite-dimensional restricted Lie algebras over a perfect field 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 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'ᵖ+γ₃(L) H/H'ᵖ+γ₃(H).