Journal of Operator Theory

Volume 58, Issue 1, Summer 2007 pp. 127-133.

Action of discrete amenable groups on real $W^*$-algebras

Authors: A.A. Rakhimov
Author institution: Department of Mathematics, Karadeniz Technical University, Trabzon, 61080, Turkey

Summary: We consider a real analogue of the result of A. Ocneanu about the actions of discrete amenable groups on W$^*$-algebras. One gives the classification up to outer conjugacy of the actions of amenable groups on the hyperfinite real factor of type II$_1$. A main result is the uniqueness up to outer conjugacy of the free action of an amenable group on the hyperfinite real factor of type II$_1$.

Keywords: Real $W^*$-algebra, action of groups on real $W^*$-algebras, discrete amenable groups

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