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.
From subfactors to categories and topology
5 Pith papers cite this work. Polarity classification is still indexing.
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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.
Defines NI-SETOs as relative centers of unitary fusion categories and shows they can be realized in string net models and on boundaries of 3D Walker-Wang models.
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
Parafermionization equates the Monster CFT to a gauged parafermion pair, yielding Rep(so(3)_p) symmetry and defect McKay-Thompson series invariant under Gamma_1(p+2).
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Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.