Geodesic
Classification for the  Actions of a Compact Abelian Group on a Semifinite Real $W^*$-Algebra
Matematičeskie trudy, Tome 3 (2000) no. 2, pp. 171-181 
A. A. Rakhimov. Classification for the  Actions of a Compact Abelian Group on a Semifinite Real $W^*$-Algebra. Matematičeskie trudy, Tome 3 (2000) no. 2, pp. 171-181. http://geodesic.mathdoc.fr/item/MT_2000_3_2_a6/
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     author = {A. A. Rakhimov},
     title = {Classification for the~ {Actions} of {a~Compact} {Abelian} {Group} on {a~Semifinite} {Real} $W^*${-Algebra}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {171--181},
     year = {2000},
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     url = {http://geodesic.mathdoc.fr/item/MT_2000_3_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, we study the actions of groups on real von Neumann algebras. A complete classification is obtained for the actions of arbitrary finite groups on hyperfinite real factors of type II$_1$. Using Takesaki's theorem for real von Neumann algebras, we classify (up to conjugacy) the actions of compact abelian groups on hyperfinite real factor of type II$_\infty$ in terms of cocycle-conjugacy of dual actions.