Skew Commutators and Lie Isomorphisms in Real von Neumann Algebras

In this paper we study skew elementsRkand their commutators in a real factorR, and prove that ifRandSare real factors not of typeI1andI2then derived Lie algebras [Rk, Rk] and [Sk, Sk] are isomorphic if and only ifRandSare *-isomorphic.