Modular invariants for group-theoretical modular data. I
Alexei Davydov
TL;DR
This paper classifies algebraic structures in group-theoretical modular categories to describe modular invariants and determine when such categories are equivalent as ribbon categories.
Contribution
It provides a classification of indecomposable commutative separable algebras and local modules, offering new insights into modular invariants and category equivalences.
Findings
Classification of indecomposable commutative separable algebras
Description of modular invariants for group-theoretical data
Criteria for equivalence of group-theoretical modular categories
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Operator Algebra Research