Geodesic
Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 132-148 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Actions of groups on pure infinite real factors are considered. Actions of discrete amenable group on an injective real factor of type $\mathrm{III}_\lambda$ ($\lambda\ne1$) are classified up to cocycle conjugacy. 
@article{ZNSL_2004_315_a9,
     author = {A. A. Rakhimov},
     title = {Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {132--148},
     year = {2004},
     volume = {315},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a9/}
}
TY  - JOUR
AU  - A. A. Rakhimov
TI  - Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2004
SP  - 132
EP  - 148
VL  - 315
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a9/
LA  - ru
ID  - ZNSL_2004_315_a9
ER  - 
%0 Journal Article
%A A. A. Rakhimov
%T Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$
%J Zapiski Nauchnykh Seminarov POMI
%D 2004
%P 132-148
%V 315
%U http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a9/
%G ru
%F ZNSL_2004_315_a9
A. A. Rakhimov. Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 32, Tome 315 (2004), pp. 132-148. http://geodesic.mathdoc.fr/item/ZNSL_2004_315_a9/

[1] P. J. Stacey, “Real structure in $\sigma$-finite factors of type $III_\lambda$ where $0\lambda1$”, Proc. London Math. Soc. 3, 47 (1983), 275–284 | DOI | MR | Zbl

[2] Sh. M. Usmanov, “Klassifikatsiya veschestvennykh $W^*$-faktorov tipa $III_\lambda$, $\lambda{\in}(0,1)$”, Funktsionalnyi analiz i ego prilozheniya, 19:3 (1985), 94–95 | MR | Zbl

[3] Sh. M. Usmanov, “Continuous decomposition of real von Neumann algebras of type III”, Algebra and Operator Theory. Proc. Coll., Kluwer Acad. Pub., 1998, 111–116 | MR | Zbl

[4] A. Connes, “Classification of automorphisms of hyperfinite factors of type $II_1$ and $II_{\infty}$, and application to type III factors”, Bull. Amer. Math. Soc., 81:6 (1975), 1090–1092 | DOI | MR | Zbl

[5] A. Connes, “Outer conjugacy classes of automorphisms of factors”, Ann. Scient. Ec. Norm. Sup., $4^e$ serie, 8 (1975), 383–420 | MR

[6] V. Jones, Actions of finite groups on the hyperfinite type $II_1$ factor, Mem. Amer. Math. Soc., 28, no. 237, 1980 | MR

[7] V. Jones, M. Takesaki, “Actions of compact abelian groups on semifinite injective factors”, Acta Math., 153 (1984), 213–258 | DOI | MR | Zbl

[8] A. Ocneanu, “Actions of discrete amenable groups on factors”, Lect. Notes Math., 1138, Springer, Berlin, 1985 | MR | Zbl

[9] C. E. Sutherland, M. Takesaki, “Actions of discrete amenable groups on injective factors of type $III_\lambda$, $\lambda\not=1$”, Pacific J. Math., 137:2 (1989), 405–444 | MR | Zbl

[10] A. A. Rakhimov, Sh. M. Usmanov, “Periodicheskie $\ast$-avtomorfizmy i $\ast$-antiavtomorfizmy in'ektivnykh faktorov”, Funktsionalnyi analiz i ego prilozheniya, 29:1 (1995), 87–89 | MR | Zbl

[11] A. A. Rakhimov, Sh. M. Usmanov, “Outer conjugacy classes of automorphisms and antiautomorphisms of real and complex injective factors”, J. Funct. Anal., 144 (1997), 475–485 | DOI | MR | Zbl

[12] A. A. Rakhimov, “Actions of finite groups on the hyperfinite real type $II_1$ factor”, Methods of Functional Analysis and Topology, 4:3 (1998), 72–88 | MR

[13] A. A. Rakhimov, “Classification for actions of compact abelian group on semifinite real $W^*$-algebra”, Siberian Advances in Mathematics, 11:2 (2001), 83–93 | MR | Zbl

[14] Katayama, C. E. Sutherland, M. Takesaki, “Actions of discrete amenable groups on injective factors of type $III_1$”, Invent. Math., 132 (1998), 331–380 | DOI | MR | Zbl

[15] M. Takesaki, Theory of operator algebras, I, Springer-Verlag, Berlin, 1979 | MR

[16] J. Feldman, P. Hahn, C. C. Moore, “Orbit structure and countable sections for action of continuous groups”, J. Funct. Anal., 28:3 (1978), 186–230 | MR | Zbl

[17] A. Ramsay, “Topologies on measured groupoids”, J. Funct. Anal., 47:3 (1982), 314–343 | DOI | MR | Zbl

[18] T. Giordano, Antiautomorphismes involutifs des facteurs de von Neumann injectifs, These, Universite de Neuchatel, 1981

[19] A. A. Rakhimov, “O deistvi diskretnoi amenabelnoi gruppy na veschestvennykh faktorakh”, Dokl. AN RUz., v pechati

[20] Sh. A. Ayupov, A. A. Rakhimov, Sh. M. Usmanov, Jordan, Real, and Lie structures in operator algebras, 418, Kluwer Academic Publishers, MAIA, 1997 | MR | Zbl

[21] A. Connes, M. Takesaki, “The flow of weights on factors of type III”, Thoku Math. J., 29:2 (1977), 473–575 | DOI | MR | Zbl

[22] A. Connes, “Une classification des facteurs de type III”, Ann. Sc. Ec. Norm. Sup., 6 (1973), 133–252 | MR | Zbl

[23] Y. Nakagami, “Dual action on a von Neumann algebras and Takesaki duality theorem for a locally compact group”, Publ. RIMS., Kyoto Univ., 12 (1977), 727–775 | DOI | MR | Zbl

[24] Y. Nakagami, M. Takesaki, Duality for crossed products of von Neumann algebras, Springer Lect. Notes Math., 731, 1979 | MR | Zbl

[25] M. Takesaki, “Duality for crossed products and the structure of von Neumann algebras of type, III”, Acta Math., 131 (1973), 249–310 | DOI | MR | Zbl

[26] Sh. M. Usmanov, Nepreryvnoe i diskretnoe razlozheniya veschestvennykh $W^*$-algebr i ikh uslovnye ozhidaniya i operatornoznachnye vesa, Doktorskaya disser., Tashkent, 1999

[27] T. Giordano, “Antiautomorphismes involutifs des facteurs de von Neumann injectifs, II”, J. Funct. Anal., 51:3 (1983), 326–360 | DOI | MR | Zbl

[28] U. Haagerup, E. Stormer, “Pointwise inner automorphisms of von Neumann algebras, with an appendix by C. Sutherland”, J. Funct. Anal., 92 (1990), 177–201 | DOI | MR | Zbl