Proves equivalence (Rep^G(A))^G ≅ Rep(A^G) as balanced W*-tensor categories for general (not necessarily rational) conformal nets A with faithful finite group G action, generalizing the rational case and including balances.
[DHR71] Sergio Doplicher, Rudolf Haag, and John E
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Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
For any finite group G there exists a McDuff II1 factor M such that its categorical Connes tilde-chi(M) is braided equivalent to Rep(G), providing the first non-modular braided fusion category realized this way.
Rep^G(A) for a conformal net A with discrete group G action is canonically a G-crossed balanced W*-tensor category.
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Balanced tensor categories of representations of fixed-points conformal nets
Proves equivalence (Rep^G(A))^G ≅ Rep(A^G) as balanced W*-tensor categories for general (not necessarily rational) conformal nets A with faithful finite group G action, generalizing the rational case and including balances.
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Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
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String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
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For any finite group G there exists a McDuff II1 factor M such that its categorical Connes tilde-chi(M) is braided equivalent to Rep(G), providing the first non-modular braided fusion category realized this way.
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Twisted representations of conformal nets and crossed balanced tensor categories
Rep^G(A) for a conformal net A with discrete group G action is canonically a G-crossed balanced W*-tensor category.