Modular invariants for group-theoretical modular data. I

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...

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Bibliographic Details
Published in:Journal of algebra 2010-03, Vol.323 (5), p.1321-1348
Main Author: Davydov, Alexei
Format: Article
Language:English
Subjects:
Modular categories
Modular invariants
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2009.11.041