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Derived Ring Isomorphisms of Von Neumann Algebras

Published online by Cambridge University Press:  20 November 2018

C. Robert Miers
C. Robert Miers*
Affiliation:
University of Victoria, Victoria, British Columbia
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 6 , December 1973 , pp. 1254 - 1268
Copyright
Copyright © Canadian Mathematical Society 1973

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