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.


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


[1] Connes, A., A factor of type II with countable fundamental groups, J. Operator Theory, 4, 151-153 (1980) · Zbl 0455.46056
[2] Connes, A.; Jones, V., A \(II_1\)-factor with two nonconjugate Cartan subalgebras, Bull. Amer. Math. Soc., 6, 211-212 (1982) · Zbl 0501.46056
[3] Choda, M., Crossed products and property \(T\), Math. Jap., 26, 557-567 (1981) · Zbl 0477.46048
[4] Choda, M.; Watatani, I., Fixed point algebra and property \(T\), Math. Japon., 27, 263-266 (1982) · Zbl 0486.46048
[5] Haagerup, U., The standard form of von Neumann algebras, Math. Scand., 32, 271-283 (1976) · Zbl 0304.46044
[6] Segal, I. E., A non-commutative extension of abstract integration, Ann. of Math., 57, 401-457 (1953) · Zbl 0051.34201
[7] Connes, A., Almost periodic states and factors of type III, J. Funct. Anal., 16, 415-445 (1974) · Zbl 0302.46050
[8] Bezuglyi, S. I.; Golodets, V. Ya, Hyperfinite and \(II_1\) actions for nonamenable group, J. Funct. Anal., 39, 30-40 (1981) · Zbl 0496.22011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.