Acta Mathematica

, 191:225 | Cite as

Universal properties ofL(F ) in subfactor theory

  • Sorin Popa
  • Dimitri Shlyakhtenko
Article

References

  1. [D1]
    Dykema, K., Free products of hyperfinite von Neumann algebras and free dimension.Duke Math. J., 69 (1993), 97–119.CrossRefMATHMathSciNetGoogle Scholar
  2. [D2]
    —, Interpolated free group factors.Pacific J. Math., 163 (1994), 123–135.MATHMathSciNetGoogle Scholar
  3. [D3]
    —, Amalgamated free products of multi-matrix algebras and a construction of subfactors of a free group factor.Amer. J. Math., 117 (1995), 1555–1602.MATHMathSciNetGoogle Scholar
  4. [DR]
    Dykema, K. &Râdulescu, F., Compressions of free products of von Neumann algebras.Math. Ann., 316 (2000), 61–82.CrossRefMathSciNetMATHGoogle Scholar
  5. [J1]
    Jones, V. F. R., Index for subfactors.Invent. Math., 72 (1983), 1–25.CrossRefMATHMathSciNetGoogle Scholar
  6. [J2]
    Jones, V. F. R., Planar algebras. Preprint, Berkeley, 1999.Google Scholar
  7. [P1]
    Popa, S., Markov traces on universal Jones algebras and subfactors of finite index.Invent. Math., 111 (1993), 375–405.CrossRefMATHMathSciNetGoogle Scholar
  8. [P2]
    —, Classification of amenable subfactors of type II.Acta Math., 172 (1994), 163–255.MATHMathSciNetGoogle Scholar
  9. [P3]
    —, An axiomatization of the lattice of higher relative commutants of a subfactor.Invent. Math., 120 (1995), 427–445.CrossRefMATHMathSciNetGoogle Scholar
  10. [P4]
    —,Classification of Subfactors and Their Endomorphisms. CBMS Regional Conf. Ser. in Math., 86. Amer. Math. Soc., Providence, RI, 1995.MATHGoogle Scholar
  11. [P5]
    —, Universal construction of subfactors.J. Reine Angew. Math., 543 (2002), 39–81.MATHMathSciNetGoogle Scholar
  12. [R1]
    Râdulescu, F., A one-parameter group of automorphisms of λ(F B(H) scaling the trace.C. R. Acad. Sci. Paris Sér. I Math., 314 (1992), 1027–1032.MATHGoogle Scholar
  13. [R2]
    —, 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.CrossRefMathSciNetMATHGoogle Scholar
  14. [S1]
    Shlyakhtenko, D., Free quasi-free states.Pacific J. Math., 177 (1997), 329–368.MATHMathSciNetCrossRefGoogle Scholar
  15. [S2]
    —, Some applications of freeness with amalgamation.J. Reine Angew. Math., 500 (1998), 191–212.MATHMathSciNetGoogle Scholar
  16. [S3]
    —, A-valued semicircular systems.J. Funct. Anal., 166 (1999), 1–47.CrossRefMATHMathSciNetGoogle Scholar
  17. [SU]
    Shlyakhtenko, D. &Ueda, Y., Irreducible subfactors ofL(F ) of index λ>4.J. Reine Angew. Math., 548 (2002), 149–166.MathSciNetMATHGoogle Scholar
  18. [V]
    Voiculescu, D., Circular and semicircular systems and free product factors, inOperator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (Paris, 1989), pp. 45–60. Progr. Math., 92. Birkhäuser Boston, Boston, MA, 1990.Google Scholar
  19. [VDN]
    Voiculescu, D., Dykema, K., &Nica, A.,Free Random Variables. CRM Monogr. Ser., 1. Amer. Math. Soc., Providence, RI, 1992.MATHGoogle Scholar

Copyright information

© Institut Mittag-Leffler 2003

Authors and Affiliations

  • Sorin Popa
    • 1
  • Dimitri Shlyakhtenko
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

Personalised recommendations