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Rescalings of free products of II$_1$-factors


Authors: Ken Dykema and Florin Radulescu
Journal: Proc. Amer. Math. Soc. 131 (2003), 1813-1816
MSC (2000): Primary 46L09
DOI: https://doi.org/10.1090/S0002-9939-02-06749-7
Published electronically: October 1, 2002
MathSciNet review: 1955269
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Abstract: We introduce the notation $\mathcal{Q}(1)*\cdots*\mathcal{Q}(n)*L(\mathbf F_r)$ for von Neumann algebra II$_1$-factors where $r$ is allowed to be negative. This notation is defined by rescalings of free products of II$_1$-factors, and is proved to be consistent with known results and natural operations. We also give two statements which we prove are equivalent to isomorphism of free group factors.

References [Enhancements On Off] (What's this?)

  • 1. K. Dykema, Free products of hyperfinite von Neumann algebras and free dimension, Duke Math. J. 69 (1993), 97-119. MR 93m:46071
  • 2. , Interpolated free group factors, Pacific J. Math. 163 (1994), 123-135. MR 95c:46103
  • 3. , Free subproducts and free scaled products of II$_1$-factors, J. Funct. Anal. (to appear).
  • 4. K. Dykema, F. Radulescu, Compressions of free products of von Neumann algebras, Math. Ann. 316 (2000), 61-82. MR 2001f:46100
  • 5. F.J. Murray and J. von Neumann, Rings of operators. IV, Ann. of Math. 44 (1943), 716-808. MR 5:101a
  • 6. F. Radulescu, Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index, Invent. Math. 115 (1994), 347-389. MR 95c:46102

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Additional Information

Ken Dykema
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
Email: Ken.Dykema@math.tamu.edu

Florin Radulescu
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242–1466
Email: radulesc@math.uiowa.edu

DOI: https://doi.org/10.1090/S0002-9939-02-06749-7
Received by editor(s): April 3, 2001
Received by editor(s) in revised form: January 18, 2002
Published electronically: October 1, 2002
Additional Notes: The first author was partially supported by NSF grant DMS–0070558
The second author was partially supported by NSF grant DMS–9970486. Both authors also thank the Mathematical Sciences Research Institute, where they were engaged in this work. Research at MSRI is supported in part by NSF grant DMS–9701755.
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society