This article is cited in 1 paper

Classification for the Actions of a Compact Abelian Group on a Semifinite Real $W^*$-Algebra

A. A. Rakhimov

University of World Economy and Diplomacy of the Ministry of Foreign Affairs of the Republic of Uzbekistan

Abstract: 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.

Key words: real von Neumann algebra, action, dual action, stable conjugacy, cocycle-conjugacy.

UDC: 517.98

Received: 07.05.1999

 English version: Siberian Advances in Mathematics, 2001, 11:2, 83–93

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