Abstract
In this note we describe (up to isomorphism) the real von Neiman algebras R with Abelian skew-symmetric part \(R_k = \{ x \in R:x^* = - x\} \), i.e., such that xy-yx=0 for any \(x,y \in R_k \).
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Ayupov, S.A. Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part. Functional Analysis and Its Applications 36, 145–147 (2002). https://doi.org/10.1023/A:1015674624679
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DOI: https://doi.org/10.1023/A:1015674624679