Relative center construction for $G$-graded C$^*$-tensor categories and Longo-Rehren inclusions

TL;DR

This paper explores the concept of $G$-braiding in the relative Drinfeld center of $G$-graded tensor categories, linking it to Longo-Rehren inclusions to deepen understanding of their structure.

Contribution

It provides a new perspective on $G$-braiding by relating it to Longo-Rehren inclusions in the context of $G$-graded C$^*$-tensor categories.

Findings

Establishes a connection between $G$-braiding and Longo-Rehren inclusions.

Offers a new framework for understanding the structure of $G$-graded tensor categories.

Clarifies the role of relative centers in the theory of tensor categories.

Abstract

Gelaki-Naidu-Nikshych and Turaev-Virelizier showed the existence of $G$-braiding on the relative Drinfeld center of a $G$-graded tensor category. We will explain this concept from the viewpoint of Longo-Rehren inclusions.