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Modular invariants for group-theoretical modular data. I

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arxiv 0908.1044 v1 pith:DRLWXG7D submitted 2009-08-07 math.QA math.CT

Alexei Davydov This is my paper · ORCID
classification math.QAmath.CT
keywords modulargroup-theoreticalcategoriesdatainvariantsalgebrasanswerbi-product
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Algebras of order parameters in one-dimensional spin systems

    cond-mat.str-el 2026-05 unverdicted novelty 7.0 of 10

    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.

  2. Classical interpolation categories

    math.RT 2025-07 conditional novelty 7.0 of 10

    Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.

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