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Proceedings of the American Mathematical Society

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Free group factors and factors with some decompositions


Authors: Junhao Shen and Xiaoxia Zhang
Journal: Proc. Amer. Math. Soc. 133 (2005), 2267-2272
MSC (2000): Primary 46L05, 47D15
DOI: https://doi.org/10.1090/S0002-9939-05-07407-1
Published electronically: March 4, 2005
MathSciNet review: 2138869
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Abstract: In this paper, we show that if type $II_1$ 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 $l_a$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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Additional Information

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

Xiaoxia Zhang
Affiliation: Department of Mathematics, University of Yan Tai, Shan Dong 264005, People’s Republic of China
Email: zxxmath@yahoo.com.cn

DOI: https://doi.org/10.1090/S0002-9939-05-07407-1
Keywords: Free group factor, diffused algebra, hyperfinite $II_1$ factor
Received by editor(s): June 14, 2002
Received by editor(s) in revised form: April 17, 2003
Published electronically: March 4, 2005
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society