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Universal properties ofL(F ∞) in subfactor theory

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Acta Mathematica

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References

  1. Dykema, K., Free products of hyperfinite von Neumann algebras and free dimension.Duke Math. J., 69 (1993), 97–119.

    Article  MATH  MathSciNet  Google Scholar 

  2. —, Interpolated free group factors.Pacific J. Math., 163 (1994), 123–135.

    MATH  MathSciNet  Google Scholar 

  3. —, Amalgamated free products of multi-matrix algebras and a construction of subfactors of a free group factor.Amer. J. Math., 117 (1995), 1555–1602.

    MATH  MathSciNet  Google Scholar 

  4. Dykema, K. &Râdulescu, F., Compressions of free products of von Neumann algebras.Math. Ann., 316 (2000), 61–82.

    Article  MathSciNet  MATH  Google Scholar 

  5. Jones, V. F. R., Index for subfactors.Invent. Math., 72 (1983), 1–25.

    Article  MATH  MathSciNet  Google Scholar 

  6. Jones, V. F. R., Planar algebras. Preprint, Berkeley, 1999.

  7. Popa, S., Markov traces on universal Jones algebras and subfactors of finite index.Invent. Math., 111 (1993), 375–405.

    Article  MATH  MathSciNet  Google Scholar 

  8. —, Classification of amenable subfactors of type II.Acta Math., 172 (1994), 163–255.

    MATH  MathSciNet  Google Scholar 

  9. —, An axiomatization of the lattice of higher relative commutants of a subfactor.Invent. Math., 120 (1995), 427–445.

    Article  MATH  MathSciNet  Google Scholar 

  10. —,Classification of Subfactors and Their Endomorphisms. CBMS Regional Conf. Ser. in Math., 86. Amer. Math. Soc., Providence, RI, 1995.

    MATH  Google Scholar 

  11. —, Universal construction of subfactors.J. Reine Angew. Math., 543 (2002), 39–81.

    MATH  MathSciNet  Google Scholar 

  12. Râdulescu, F., A one-parameter group of automorphisms of λ(F ∞)ξB(H) scaling the trace.C. R. Acad. Sci. Paris Sér. I Math., 314 (1992), 1027–1032.

    MATH  Google Scholar 

  13. —, 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.

    Article  MathSciNet  MATH  Google Scholar 

  14. Shlyakhtenko, D., Free quasi-free states.Pacific J. Math., 177 (1997), 329–368.

    Article  MATH  MathSciNet  Google Scholar 

  15. —, Some applications of freeness with amalgamation.J. Reine Angew. Math., 500 (1998), 191–212.

    MATH  MathSciNet  Google Scholar 

  16. —, A-valued semicircular systems.J. Funct. Anal., 166 (1999), 1–47.

    Article  MATH  MathSciNet  Google Scholar 

  17. Shlyakhtenko, D. &Ueda, Y., Irreducible subfactors ofL(F ∞) of index λ>4.J. Reine Angew. Math., 548 (2002), 149–166.

    MathSciNet  MATH  Google Scholar 

  18. 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. Voiculescu, D., Dykema, K., &Nica, A.,Free Random Variables. CRM Monogr. Ser., 1. Amer. Math. Soc., Providence, RI, 1992.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, 90095, Los Angeles, CA, USA

    Sorin Popa

  2. Department of Mathematics, University of California, 90095, Los Angeles, CA, USA

    Dimitri Shlyakhtenko

Authors
  1. Sorin Popa
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  2. Dimitri Shlyakhtenko
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Popa, S., Shlyakhtenko, D. Universal properties ofL(F ∞) in subfactor theory. Acta Math. 191, 225–257 (2003). https://doi.org/10.1007/BF02392965

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  • DOI: https://doi.org/10.1007/BF02392965

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