Geodesic
Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 75-77

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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 $x,y\in R_k$.
Keywords: real von Neimann algebra, symmetric element, skew-symmetric element, $JW$-algebra, spin factor. 
@article{FAA_2002_36_2_a7,
     author = {Sh. A. Ayupov},
     title = {Description of the {Real} von {Neumann} {Algebras} with {Abelian} {Skew-Symmetric} {Part}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {75--77},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a7/}
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Sh. A. Ayupov. Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 75-77. http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a7/