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.
Modular invariants for group-theoretical modular data. I
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abstract
We classify indecomposable commutative separable (special Frobenius) algebras and their local modules in (untwisted) group-theoretical modular categories. This gives a description of modular invariants for group-theoretical modular data. As a bi-product we provide an answer to the question when (and in how many ways) two group-theoretical modular categories are equivalent as ribbon categories.
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Algebras of order parameters in one-dimensional spin systems
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.