Inventiones mathematicae

, Volume 111, Issue 1, pp 375–405

Markov traces on universal Jones algebras and subfactors of finite index

  • Sorin Popa

DOI: 10.1007/BF01231293

Cite this article as:
Popa, S. Invent Math (1993) 111: 375. doi:10.1007/BF01231293


We construct one parameter families of inclusions of nonhyperfinite type II1 factorsNsMs, with trivial relative commutant (Ns)′∩Ms=ℂ and with the Jones' index [MsNs]=s ranging over the sets∈{4 cos2π/n|n≧4}∪[4, ∞), by using Markov traces on certain universal algebras associated to a given algebra and to the Jones' sequence of projections. This solves the problem of finding all possible values of indices of subfactors with trivial relative commutant in arbitrary type II1 factors, by showing that any numbers>4 can occur.

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Sorin Popa
    • 1
  1. 1.Mathematics DepartmentUniversity of CaliforniaLos AngelesUSA