2022
DOI: 10.1007/s00023-022-01154-4
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Galois Correspondence and Fourier Analysis on Local Discrete Subfactors

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Cited by 7 publications
(4 citation statements)
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“…In the second part, we restrict ourselves to discrete conformal subnets (Definition 3.2), which also cover the case of finite index subnets (Definition 3.3). In this second part, we show that our previous analysis of local discrete subfactors [BDVG21], [BDVG22] applies to conformal subnets as well. In more detail, a quantum operation on A (Definition 4.12) is a collection of unital completely positive maps A(I) → A(I), indexed by I ⊂ S 1 , that are compatible with the inclusions of local algebras A(I) ⊂ A(J) for I ⊂ J, vacuum preserving and conformally covariant in a natural sense, and extreme in the sense of convex sets among all unital completely positive maps on A.…”
Section: Introductionmentioning
confidence: 80%
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“…In the second part, we restrict ourselves to discrete conformal subnets (Definition 3.2), which also cover the case of finite index subnets (Definition 3.3). In this second part, we show that our previous analysis of local discrete subfactors [BDVG21], [BDVG22] applies to conformal subnets as well. In more detail, a quantum operation on A (Definition 4.12) is a collection of unital completely positive maps A(I) → A(I), indexed by I ⊂ S 1 , that are compatible with the inclusions of local algebras A(I) ⊂ A(J) for I ⊂ J, vacuum preserving and conformally covariant in a natural sense, and extreme in the sense of convex sets among all unital completely positive maps on A.…”
Section: Introductionmentioning
confidence: 80%
“…An abstract convolution replaces the group operation, an involution replaces the group inversion, there is an identity element and a Haar measure (finite in the case of compact hypergroups). The key point in the proof of Theorem 6.8, besides applying our previous results on local discrete subfactors [BDVG21], [BDVG22], is to show that every B(I)-fixing unital completely positive map A(I) → A(I), for fixed I ⊂ S 1 , with no additional assumption, can be extended to a compatible, covariant and vacuum preserving family of B-fixing maps on the whole net A → A (Theorem 6.4). We don't know whether the same statement is true for arbitrary irreducible conformal inclusions (not assuming discreteness).…”
Section: Introductionmentioning
confidence: 96%
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“…The usage of modular theory in recent years in quantum information theory [11,29,30,15,54,38] and quantum field theory [61,16,32,31,13] indicates its importance. In addition, the Bayesian inverses, in the special case of faithful states given by the vacuum state, have been recently used as a notion of inversion for generalized global gauge symmetries of subfactors and local quantum field theories [6,7,8] in the algebraic setting [26].…”
Section: Introductionmentioning
confidence: 99%