Derived Ring Isomorphisms of Von Neumann Algebras

Abstract

Let M be an associative *-algebra with complex scalar field. M may be turned into a Lie algebra by defining multiplication by [A, B] = AB - BA. A Lie *-subalgebra L of M is a *-linear subspace of M such that if A, B ∈ L then [A,B] ∈ L. A Lie *-isomorphism ϕ between Lie *-subalgebras L1 and L2 of *-algebras M and N is a one-one, *-linear map of L1 onto L2 such that ϕ[A, B] = [ϕ(A), ϕ(B)] for all A , B ∈ L1.