The Structure of Sectors¶Associated with Longo–Rehren Inclusions¶I. General Theory

Izumi, Masaki

doi:10.1007/s002200000234

Cited by 97 publications

(187 citation statements)

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“…It is well known that the dual sector [θ] does not determine M uniquely up to inner conjugacy. This is an H 2 cohomological obstruction that has been studied in [31,33] where the …”

Section: Q-systems For Inclusionsmentioning

confidence: 99%

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Subfactor Realisation of Modular Invariants

Evans¹,

Pinto²

2003

Commun. Math. Phys.

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We study the problem of realising modular invariants by braided subfactors and the related problem of classifying nimreps. We develop the fusion rule structure of these modular invariants. This structure is useful tool in the analysis of modular data from quantum double subfactors, particularly those of the double of cyclic groups, the symmetric group on 3 letters and the double of the subfactors with principal graph the extended Dynkin diagram D(1) 5 . In particular for the double of S 3 , 14 of the 48 modular modular invariants are nimless, and only 28 of the remaining 34 nimble invariants can be realised by subfactors.

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“…It is well known that the dual sector [θ] does not determine M uniquely up to inner conjugacy. This is an H 2 cohomological obstruction that has been studied in [31,33] where the …”

Section: Q-systems For Inclusionsmentioning

confidence: 99%

“…This modular data can be twisted for every [k] ∈ H 3 (G, S 1 ) [14], and the subfactor interpretation of this data is in [31]. The parameter k is regarded as the level in this setting [14].…”

Section: Introductionmentioning

confidence: 99%

Subfactor Realisation of Modular Invariants

Evans¹,

Pinto²

2003

Commun. Math. Phys.

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“…For β ∈ End 0 (N ) we define β op = j • β • j −1 ∈ End 0 (N op ). We denote by B G B the unitary fusion category ρ ⊗ σ op : ρ, σ ∈ F ⊂ End 0 (B), see [LR95,Izu00]. This means, we have…”

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confidence: 99%

Generalized orbifold construction for conformal nets

Bischoff

2017

Rev. Math. Phys.

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Abstract. Let B be a conformal net. We give the notion of a proper action of a finite hypergroup acting by vacuum preserving unital completely positive (so-called stochastic) maps, which generalizes the proper actions of finite groups. Taking fixed points under such an action gives a finite index subnet B K of B, which generalizes the G-orbifold. Conversely, we show that if A ⊂ B is a finite inclusion of conformal nets, then A is a generalized orbifold A = B K of the conformal net B by a unique finite hypergroup K. There is a Galois correspondence between intermediate netsIn this case, the fixed point of B K ⊂ A is the generalized orbifold by the hypergroup of double cosets L\K/L.If A ⊂ B is an finite index inclusion of completely rational nets, we show that the inclusion A(I) ⊂ B(I) is conjugate to a Longo-Rehren inclusion. This implies that if B is a holomorphic net, and K acts properly on B, then there is a unitary fusion category F which is a categorification of K and Rep(B K

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“…Remark 3.7. Recently, Izumi has also given a concrete formula for the S and T matrices for several subfactors including the E 6 -subfactor, and has calculated TuraevViro-Ocneanu-invariants for lens spaces using sector theory [Iz3,Iz4].…”

Section: For Triangulation T Of Surface We Denote By V ( ; T ) the mentioning

confidence: 99%