On Lagrangian algebras in group-theoretical braided fusion categories

TL;DR

This paper characterizes Lagrangian algebras within twisted Drinfeld centers of finite groups, establishing a correspondence with module categories over pointed fusion categories, advancing the understanding of algebraic structures in braided fusion categories.

Contribution

It provides a complete classification of Lagrangian algebras in twisted Drinfeld centers using the full centre construction, linking them to module categories over pointed fusion categories.

Findings

Lagrangian algebras correspond to module categories over pointed fusion categories.

A 1-1 correspondence is established between Lagrangian algebras and module categories.

The full centre construction is used to describe these algebras.

Abstract

We describe Lagrangian algebras in twisted Drinfeld centres for finite groups. Using the full centre construction, we establish a 1-1 correspondence between Lagrangian algebras and module categories over pointed fusion categories.