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Published in:
Asymptotic Freeness of Gaussian Random Matrices Read chapter Read first chapter

2017 | OriginalPaper | Chapter

6. Free Group Factors and Freeness

Authors : James A. Mingo, Roland Speicher

Published in: Free Probability and Random Matrices

Publisher: Springer New York

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Abstract

The concept of freeness was actually introduced by Voiculescu in the context of operator algebras, more precisely, during his quest to understand the structure of special von Neumann algebras, related to free groups. We wish to recall here the relevant context and show how freeness shows up there very naturally and how it can provide some information about the structure of those von Neumann algebras.

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previous chapter Fluctuations and Second Order Freeness
next chapter Free Entropy χ: The Microstates Approach via Large Deviations
Literature
67.
105.
106.
R.V. Kadison, J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, vol. II (American Mathematical Society, Providence, 1997)MATH
137.
A. Nica, R. Speicher, Lectures on the Combinatorics of Free Probability. London Mathematical Society Lecture Note Series, vol. 335 (Cambridge University Press, Cambridge, 2006)
143.
M. Pimsner, D. Voiculescu, K-groups of reduced crossed products by free groups. J. Oper. Theory 8(1), 131–156 (1982)MathSciNetMATH
144.
F. Rădulescu, The fundamental group of the von Neumann algebra of a free group with infinitely many generators is \(\mathbb{R}_{+}\setminus \{0\}\). J. Am. Math. Soc. 5(3), 517–532 (1992)MathSciNetMATH
145.
F. Rădulescu, Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index. Invent. Math., 115(2), 347–389 (1994)MathSciNetCrossRefMATH
170.
M. Takesaki. Theory of Operator Algebras I (Springer, Berlin, 2002)MATH
179.
D. Voiculescu, Circular and semicircular systems and free product factors, in Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (Paris, 1989). Progress in Mathematics, vol. 92 (Birkhäuser Boston, Boston, MA, 1990), pp. 45–60
180.
Metadata
Title
Free Group Factors and Freeness
Authors
James A. Mingo
Roland Speicher
Copyright Year
2017
Publisher
Springer New York
Book
Free Probability and Random Matrices

Print ISBN: 978-1-4939-6941-8

Electronic ISBN: 978-1-4939-6942-5

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-1-4939-6942-5_6