Proceedings of the American Mathematical Society

Author(s): Junhao Shen; Xiaoxia Zhang
Journal: Proc. Amer. Math. Soc. 133 (2005), 2267-2272.
MSC (2000): Primary 46L05, 47D15
Posted: March 4, 2005
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Abstract: In this paper, we show that if type

von Neumann factors $\mathcal{M}$ have some decompositions introduced by Liming Ge and Sorin Popa, then these von Neumann factors are not isomorphic to free group factors $L(F_n) (n \geq 2)$ . Thus we have proved the number

defined by Ge and Popa bigger than 3 for all free group factors and we also extend some results of M. Stefan.

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2.: Liming Ge, Applications of free entropy to finite von Neumann algebras, Amer. J. Math. 119(1997), 467-485. MR 1439556 (98a:46074)
3.: Liming Ge, Applications of free entropy to fnite von Neumann algebras, II, Ann. Math. 147 (1998), 143-157. MR 1609522 (99c:46068)
4.: Liming Ge and Sorin Popa, On some decomposition properties for factors of type , Duke Math, 94 (1998), 79-101. MR 1635904 (99j:46070)
5.: S. Popa, Symmetric enveloping algebras, amenability and AFD properties for subfactors, Math. Res. Lett. 1(1994), 409-425. MR 1302385 (95i:46095)
6.: Marius B. Stefan, The indecomposability of free group factors over nonprime subfactors and abelian subalgebras, preprint.
7.: Dan Voiculescu, Circular and semicircular systems and free product fanctors, In: Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory (Prog. Math., vol. 92, pp. 45-60 Boston; Birkhauser 1990). MR 1103585 (92e:46124)
8.: Dan Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, II, Invent Math. 118 (1994), 411-440. MR 1296352 (96a:46117)
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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L05, 47D15

Junhao Shen
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email: junhao@math.upenn.edu

Dan Voiculescu, Circular and semicircular systems and free product factors, Operator algebras, unitary representations, enveloping algebras and invariant theory , Birkhauser, 1990, pp. 45-60.

A. Connes and V. Jones, Property T for von Neumann algebras, Bull. London Math. Soc. 17 (1985), 57-62.

Dan Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, II, Invent Math. 118 (1994), 411-440.

Sorin Popa, Symmetric enveloping algebras, amenability and AFD properties for subfactors, Math. Res. Lett. 1 (1994), 409-425.

Dan Voiculescu, the analogues of entropy and of Fisher's information measure in free probability theory, III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6 (1996), 172-199.

Liming Ge, Applications of free entropy to finite von Neumann algebras, Amer. J. Math. 119 (1997), 467-485.

Liming Ge , Applications of free entropy to finite von Neumann algebras, II, Ann. Math 147 (1998), 143-157.

Liming Ge and Sorin Popa, On some decoposition properties for factors of type II_1, Duke Math. 94 (1998), 79-101.

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