On the method of constructing irreducible finite index subfactors of popa

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Abstract

Let US(Q) be the universal Jones algebra associated to a finite von Neumann algebra Q and Rs ⊂ R be the Jones subfactors, s ∈ {4cos2 πn/|n ≥ 3} ∪ [4, ∞). We consider for any von Neumann subalgebra Q0 ⊂ Q the algebra US(Q, Q0) defined as the quotient of US(Q) through its ideal generated by [Q0, R] and we construct a Markov trace on US(Q, Q0). If E(Q) ∩ E(Q0) = C and Q contains n ≥ s + I unitaries u1 = 1, u2, …, un, with EQ0(ui*Uj) = δij1, 1 ≤ i, j ≤ n, then we get a family of irreducible inclusions of type IIi factors Ns ⊂ Ms, with [Ms: Ns] = s and minimal higher relative commutant. Although these subfactors are nonhyperfinite, they have the Haagerup approximation property whether Q0 ⊂ Q is a Haagerup inclusion and if either Q0 is finite dimensional or Q0 ⊂ E(Q).

Original languageEnglish (US)
Pages (from-to)201-231
Number of pages31
JournalPacific Journal of Mathematics
Volume161
Issue number2
DOIs
StatePublished - Dec 1993
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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