On M\"{u}ger's centralizer for a certain class of braided fusion categories

TL;DR

This paper derives a general formula for Mueger's centralizer in braided fusion categories containing a Tannakian subcategory, enabling a comprehensive understanding of centralizers in group-theoretical contexts.

Contribution

It introduces a new formula for Mueger's centralizer applicable to a broad class of braided fusion categories with Tannakian subcategories.

Findings

Provides a formula for Mueger's centralizer in categories with Tannakian subcategories.

Describes Mueger's centralizer for all subcategories in group-theoretical braided fusion categories.

Enhances understanding of the structure of braided fusion categories.

Abstract

We provide a general formula for Mueger's centralizer of any fusion subcategory of a braided fusion category containing a tannakian subcategory. This entails a description for Mueger's centralizer of all fusion subcategories of a group theoretical braided fusion category.