Abstract
We construct one parameter families of inclusions of nonhyperfinite type II1 factorsN s⊂M s, with trivial relative commutant (N s)′∩M s=ℂ and with the Jones' index [M s∶N s]=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.
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This work was partially supported by an NSF grant DMS-8908281
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Popa, S. Markov traces on universal Jones algebras and subfactors of finite index. Invent Math 111, 375–405 (1993). https://doi.org/10.1007/BF01231293
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DOI: https://doi.org/10.1007/BF01231293