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T-property and nonisomorphic full factors of types II and III. (English) Zbl 0614.46053

The paper deals with the actions of T-groups on von Neumann hyperfinite algebras. It is proved that there exist factors of type II with various countable fundamental groups and hence various actions. The results obtained are used to prove the existence of nonisomorphic full factors of type III\(_ 1\) with a fixed Connes invariant Sd.
Here are two of the results proved in the paper.
1. For any given countable subgroup \(\Gamma \subset {\mathbb{R}}^*_+\) there exists a factor \(M\) of type II with the countable fundamental group \(F(M)\), so that F(M)\(\supset \Gamma.\)
2. Any T(ICC)-group has a continuum of nonequivalent actions onto hyperfinite factors of type II.

MSC:

46L35 Classifications of \(C^*\)-algebras
46L55 Noncommutative dynamical systems
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References:

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