Rescalings of free products of II$_1$–factors
HTML articles powered by AMS MathViewer
- by Ken Dykema and Florin Rădulescu PDF
- Proc. Amer. Math. Soc. 131 (2003), 1813-1816 Request permission
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
- Ken Dykema, Free products of hyperfinite von Neumann algebras and free dimension, Duke Math. J. 69 (1993), no. 1, 97–119. MR 1201693, DOI 10.1215/S0012-7094-93-06905-0
- Ken Dykema, Interpolated free group factors, Pacific J. Math. 163 (1994), no. 1, 123–135. MR 1256179, DOI 10.2140/pjm.1994.163.123
- K. Dykema, Free subproducts and free scaled products of II$_1$–factors, J. Funct. Anal. (to appear).
- Kenneth J. Dykema and Florin Rădulescu, Compressions of free products of von Neumann algebras, Math. Ann. 316 (2000), no. 1, 61–82. MR 1735079, DOI 10.1007/s002080050004
- Albert Eagle, Series for all the roots of a trinomial equation, Amer. Math. Monthly 46 (1939), 422–425. MR 5, DOI 10.2307/2303036
- Florin Rădulescu, Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index, Invent. Math. 115 (1994), no. 2, 347–389. MR 1258909, DOI 10.1007/BF01231764
Additional Information
- Ken Dykema
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
- MR Author ID: 332369
- Email: Ken.Dykema@math.tamu.edu
- Florin Rădulescu
- Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242–1466
- Email: radulesc@math.uiowa.edu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1813-1816
- MSC (2000): Primary 46L09
- DOI: https://doi.org/10.1090/S0002-9939-02-06749-7
- MathSciNet review: 1955269