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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2002},
     volume = {36},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a7/}
}
TY  - JOUR
AU  - Sh. A. Ayupov
TI  - Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2002
SP  - 75
EP  - 77
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a7/
LA  - ru
ID  - FAA_2002_36_2_a7
ER  - 
%0 Journal Article
%A Sh. A. Ayupov
%T Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2002
%P 75-77
%V 36
%N 2
%U http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a7/
%G ru
%F FAA_2002_36_2_a7
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/

[1] Ayupov Sh. A., Rakhimov A. A., Usmanov Sh. M., Jordan, Real and Lie Structures in Operator Algebras, Mathematics and its Applications, 418, Kluwer Acad. Publ., Dordrecht, 1997 | MR | Zbl

[2] Stormer E., “On anti-automorphisms of von Neumann algebras”, Pacific J. Math., 21:2 (1967), 349–370 | DOI | MR

[3] Topping D., Jordan algebras of self-adjoint operators, Mem. Amer. Math. Soc., 53, 1965 | MR | Zbl

[4] Li Minli, Li-Bingren, Acta Math. Sinica, 14:1 (1998), 85–90 | DOI | MR | Zbl

[5] Ayupov Sh. A., Rakhimov A. A., Abduvaitov A. Kh., Dokl. AN RUz, 2001, no. 5

[6] Putnam C. R., “On normal operators in Hilbert space”, Amer. J. Math., 73 (1951), 357–362 | DOI | MR | Zbl

[7] Stacey P. J., “${\rm I}_{2}$ $JBW$-algebras”, Quart J. Math. Oxford, 33:129 (1982), 115–127 | DOI | MR

[8] Robertson A. G., “Automorphisms of spin factors and the decomposition of positive maps”, Quart. J. Math. Oxford, 34:133 (1983), 87–96 | DOI | MR | Zbl

[9] Ayupov Sh. A., Azamov N. A., “Commutators and Lie isomorphisms of skew elements in prime operator algebras”, Comm. Algebra, 24:4 (1996), 1501–1520 | DOI | MR | Zbl