Index theory for real factors
Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 12-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The notion of index for arbitrary real factors is introduced and investigated. The main tool in our approach is the reduction of real factors to involutive $*$-antiautomorphisms of their complex enveloping von Neumann algebras. Similarly to the complex case the values of the index for real factors are calculated.
@article{EMJ_2012_3_2_a1,
     author = {S. Albeverio and Sh. A. Ayupov and A. A. Rakhimov and R. A. Dadakhodjaev},
     title = {Index theory for real factors},
     journal = {Eurasian mathematical journal},
     pages = {12--20},
     year = {2012},
     volume = {3},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a1/}
}
TY  - JOUR
AU  - S. Albeverio
AU  - Sh. A. Ayupov
AU  - A. A. Rakhimov
AU  - R. A. Dadakhodjaev
TI  - Index theory for real factors
JO  - Eurasian mathematical journal
PY  - 2012
SP  - 12
EP  - 20
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a1/
LA  - en
ID  - EMJ_2012_3_2_a1
ER  - 
%0 Journal Article
%A S. Albeverio
%A Sh. A. Ayupov
%A A. A. Rakhimov
%A R. A. Dadakhodjaev
%T Index theory for real factors
%J Eurasian mathematical journal
%D 2012
%P 12-20
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a1/
%G en
%F EMJ_2012_3_2_a1
S. Albeverio; Sh. A. Ayupov; A. A. Rakhimov; R. A. Dadakhodjaev. Index theory for real factors. Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 12-20. http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a1/

[1] S. Albeverio, Sh. A. Ayupov, A. A. Rakhimov, R. A. Dadakhodjaev, Index for Finite Real Factors, Preprint SFB611, No 458, the Universität Bonn (Institut für Numerische Simulation, Institut für Angewandte Mathematik, Mathematisches Institut), BONN, 2009, 26 pp. ; See also: Cornell University, arXiv.org, Mathematics, Operator Algebras, arXiv: 0902.1152v1 | MR

[2] S. Albeverio, Sh. A. Ayupov, A. A. Rakhimov, R. A. Dadakhodjaev, “On Jones' Index for Real $W^*$-algebras”, Eurasian Math. J., 1:4 (2010), 5–19 | MR | Zbl

[3] Sh. A. Ayupov, Classification and representation of ordered Jordan algebras, Fan, Tashkent, 1986 | MR | Zbl

[4] Sh. A. Ayupov, A. A. Rakhimov, Real $W^*$-algebras, Actions of groups and Index theory for real factors, VDM Publishing House Ltd., Beau-Bassin, Mauritius, 2010, 138

[5] Sh. A. Ayupov, A. A. Rakhimov, Sh. M. Usmanov, Jordan, Real and Lie Structures in Operator Algebras, MAIA, 418, Kluw. Acad. Pub., 1997, 235 pp. | MR | Zbl

[6] A. Connes, “Spatial theory of von Neumann algebras”, J. Funct. Anal., 35 (1980), 153–164 | DOI | MR | Zbl

[7] T. Giordano, Antiautomorphismes involutifs des facteurs de von Neumann injectifs, Thèse, Universite de Neuchâtel, 1981, 106 pp.

[8] U. Haagerup, “Operator valued weights in von Neumann algebras, I”, J. Funct. Anal., 32 (1979), 175–206 | DOI | MR | Zbl

[9] V. F. R. Jones, “Index for Subfactors”, Inventiones Math., 72 (1983), 1–25 | DOI | MR | Zbl

[10] H. Kosaki, “Extension of Jones' Theory on index to arbitrary factors”, J. Funct. Anal., 66 (1986), 123–140 | DOI | MR | Zbl

[11] H. Kosaki, “A remark on the minimal index of subfactors”, J. Funct. Anal., 107 (1992), 458–470 | DOI | MR | Zbl

[12] P. H. Loi, “On the theory of index for type III factors”, J. Operator Theory, 28 (1992), 251–265 | MR | Zbl

[13] R. Longo, “Minimal index and Braided Subfactors”, J. Funct. Anal., 109 (1992), 98–112 | DOI | MR | Zbl

[14] F. J. Murray, J. von Neumann, “On rings of operators”, Ann. Math., 37 (1936), 116–229 | DOI | MR | Zbl

[15] A. A. Rakhimov, Y. Kesicioğlu, M. N. Cansu, “Index for real factors”, Itogi Nauki. Southern Federal Region. Research on the mathematical analysis, 3, Vladikavkaz, 2009, 200–212

[16] A. A. Rakhimov, “Index for finite real factors”, Abstracts of the third congress of the world mathematical society of turkic countries (June 30 – July 4, 2009, Almaty, “Kazak universiteti”), v. 1, 127

[17] A. A. Rakhimov, T. Kör, Y. Kesicioğlu, “Index for Finite Real Factors”, XX Ulusal Matematik Sempozyumu, Bildiri özetleri (5–8 Eylül, 2007, Atatürk Üniversitesi, Erzurum)

[18] A. A. Rakhimov, “Injective real $W^*$-factors of type $\mathrm{III}_\lambda$, $0\lambda1$”, Funct. Anal. and its Applications, 3:2 (1997), 41–45 | MR | Zbl

[19] Sh. M. Usmanov, “Operator-valued weights on real $W^*$-algebras and reversible JW-algebras”, Sbornik: Mathematics, 190:10 (1999), 1505–1522 | DOI | MR | Zbl

[20] Sh. M. Usmanov, “Conditional expectations on real $W^*$-algebras and JW-algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2001, no. 7, 43–47 | MR | Zbl