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110
The Structure of Sectors Associated with the LongoRehren Inclusions I. General Theory
 Commun. Math. Phys
, 1999
"... We investigate the structure of the LongoRehren inclusion for a finite closed system of endomorphisms of factors, whose categorical structure is known to be the same as the asymptotic inclusion of A. Ocneanu. In particular, we obtain a precise description of the sectors associated with the LongoRe ..."
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Cited by 76 (1 self)
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We investigate the structure of the LongoRehren inclusion for a finite closed system of endomorphisms of factors, whose categorical structure is known to be the same as the asymptotic inclusion of A. Ocneanu. In particular, we obtain a precise description of the sectors associated with the LongoRehren
Orbifold aspects of the LongoRehren subfactors
, 2008
"... In this article, we will prove that the subsectors of αinduced sectors for M ⋊ ˆ G ⊃ M forms a modular category, where M ⋊ ˆ G is the crossed product of M by the group dual ˆ G of a finite group G. In fact, we will prove that it is equivalent to Müger’s crossed product. By using this identificati ..."
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this identification, we will exhibit an orbifold aspect of the quantum double of ∆(not necessarily nondegenerate) obtained from a LongoRehren inclusion A ⊃ B ∆ under certain assumptions. We will apply the above description of the quantum double of ∆ to the ReshetikhinTuraev topological invariant of closed 3
Generalized LongoRehren subfactors and αinduction
 Comm. Math. Phys
, 2002
"... We study the recent construction of subfactors by Rehren which generalizes the LongoRehren subfactors. We prove that if we apply this construction to a nondegenerately braided subfactor N ⊂ M and α ±induction, then the resulting subfactor is dual to the LongoRehren subfactor M ⊗ M opp ⊂ R arisin ..."
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Cited by 6 (2 self)
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We study the recent construction of subfactors by Rehren which generalizes the LongoRehren subfactors. We prove that if we apply this construction to a nondegenerately braided subfactor N ⊂ M and α ±induction, then the resulting subfactor is dual to the LongoRehren subfactor M ⊗ M opp ⊂ R
Multiinterval subfactors and modularity of representations in conformal field theory
 Commun. Math. Phys
"... Dedicated to John E. Roberts on the occasion of his sixtieth birthday We describe the structure of the inclusions of factors A(E) ⊂A(E ′ ) ′ associated with multiintervals E ⊂ R for a local irreducible net A of von Neumann algebras on the real line satisfying the split property and Haag duality. I ..."
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Cited by 112 (37 self)
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. In particular, if the net is conformal and the subfactor has finite index, the inclusion associated with two separated intervals is isomorphic to the LongoRehren inclusion, which provides a quantum double construction of the tensor category of superselection sectors of A. As a consequence, the index of A(E) ⊂A
Modular Invariants, Graphs and αInduction for Nets of Subfactors I
, 2008
"... We analyze the induction and restriction of sectors for nets of subfactors defined by Longo and Rehren. Picking a local subfactor we derive a formula which specifies the structure of the induced sectors in terms of the original DHR sectors of the smaller net and canonical endomorphisms. We also obta ..."
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Cited by 104 (17 self)
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We analyze the induction and restriction of sectors for nets of subfactors defined by Longo and Rehren. Picking a local subfactor we derive a formula which specifies the structure of the induced sectors in terms of the original DHR sectors of the smaller net and canonical endomorphisms. We also
DRINFELD CENTER AND REPRESENTATION THEORY FOR MONOIDAL CATEGORIES
"... Abstract. Motivated by the relation between the Drinfeld double and central property (T) for quantum groups, given a rigid C∗tensor category C and a unitary halfbraiding on an indobject, we construct a ∗representation of the fusion algebra of C. This allows us to present an alternative approach ..."
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over another II1factor obtained by the Longo–Rehren construction. As an application, we obtain an alternative proof of the result of Popa and Vaes stating that property (T) for the category defined by an extremal finite index subfactor N ⊂M is equivalent to Popa’s property (T) for the corresponding SEinclusion
Wiesbrock: A comment on Jones inclusions with infinite index, contribution to this volume
"... (dedicated to Bert Schroer’s 60th birthday) Given an irreducible inclusion of infinite vonNeumannalgebras N ⊂ M together with a conditional expectation E: M → M such that the inclusion has depth 2, we show quite explicitely how N can be viewed as the fixed point algebra of M w.r.t. an outer action ..."
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Cited by 6 (4 self)
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(dedicated to Bert Schroer’s 60th birthday) Given an irreducible inclusion of infinite vonNeumannalgebras N ⊂ M together with a conditional expectation E: M → M such that the inclusion has depth 2, we show quite explicitely how N can be viewed as the fixed point algebra of M w.r.t. an outer
DOI 10.1007/s1100501003846 Lett Math Phys (2010) 92:99–108 On the Jones Index Values for Conformal Subnets
, 2010
"... Abstract. We consider the smallest values taken by the Jones index for an inclusion of local conformal nets of von Neumann algebras on S1 and show that these values are quite more restricted than for an arbitrary inclusion of factors. Below 4, the only noninteger admissible value is 4 cos2 π/10, w ..."
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Abstract. We consider the smallest values taken by the Jones index for an inclusion of local conformal nets of von Neumann algebras on S1 and show that these values are quite more restricted than for an arbitrary inclusion of factors. Below 4, the only noninteger admissible value is 4 cos2 π/10
Results 1  10
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110