# Modular invariants for group-theoretical modular data. I

## 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.

## Key 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.