Advertisement

Free Group Factors and Freeness

Chapter
  • 1.8k Downloads
Part of the Fields Institute Monographs book series (FIM, volume 35)

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.

References

  1. 67.
    K. Dykema, Interpolated free group factors. Pac. J. Math. 163(1), 123–135 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 105.
    V.F.R. Jones, Index for subfactors. Invent. Math. 72(1), 1–25 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 106.
    R.V. Kadison, J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, vol. II (American Mathematical Society, Providence, 1997)zbMATHGoogle Scholar
  4. 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)Google Scholar
  5. 143.
    M. Pimsner, D. Voiculescu, K-groups of reduced crossed products by free groups. J. Oper. Theory 8(1), 131–156 (1982)MathSciNetzbMATHGoogle Scholar
  6. 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)MathSciNetzbMATHGoogle Scholar
  7. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 170.
    M. Takesaki. Theory of Operator Algebras I (Springer, Berlin, 2002)zbMATHGoogle Scholar
  9. 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. 45–60Google Scholar
  10. 180.
    D. Voiculescu, Limit laws for random matrices and free products. Invent. Math. 104(1), 201–220 (1991)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada
  2. 2.FB MathematikUniversität des SaarlandesSaarbrückenGermany

Personalised recommendations