## Abstract

Let US(Q) be the universal Jones algebra associated to a finite von Neumann algebra Q and R^{s} ⊂ R be the Jones subfactors, s ∈ {4cos^{2} πn/|n ≥ 3} ∪ [4, ∞). We consider for any von Neumann subalgebra Q_{0} ⊂ Q the algebra U^{S}(Q, Q_{0}) defined as the quotient of U^{S}(Q) through its ideal generated by [Q_{0}, R] and we construct a Markov trace on U^{S}(Q, Q_{0}). If E(Q) ∩ E(Q_{0}) = C and Q contains n ≥ s + I unitaries u^{1} = 1, u_{2}, …, u_{n}, with E_{Q0}(u_{i}*U_{j}) = δ_{ij}1, 1 ≤ i, j ≤ n, then we get a family of irreducible inclusions of type IIi factors N^{s} ⊂ M^{s}, with [M^{s}: N^{s}] = s and minimal higher relative commutant. Although these subfactors are nonhyperfinite, they have the Haagerup approximation property whether Q_{0} ⊂ Q is a Haagerup inclusion and if either Q_{0} is finite dimensional or Q_{0} ⊂ E(Q).

Original language | English (US) |
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Pages (from-to) | 201-231 |

Number of pages | 31 |

Journal | Pacific Journal of Mathematics |

Volume | 161 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1993 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics