Multiplicative *-Lie isomorphisms between von Neumann algebras

Let ℳ, 𝒩 be von Neumann algebras with no central summands of type I1 or I2. If Φ : ℳ → 𝒩 is a multiplicative *-Lie isomorphism, then there is a central projection E ∈ 𝒩 such that modulo a centre-valued map which annihilates commutators, EΦ is a linear Lie *-homomorphism and (I − E)Φ is a conjugate linear Lie *-homomorphism.