- BIMSA 拓扑量子场论与高对称性讨论班

Generalized Tube Algebras for 2D Gapped Phases in Turaev–Viro TQFT

组织者

白岸斯 , 陈群皓 , 孔良 , 王亦龙 , 张智浩 , 郑浩

演讲者

贾治安

时间

2026年05月19日 14:00 至 15:30

地点

A3-3-201

线上

Zoom 559 700 6085 (BIMSA)

摘要

Two-dimensional non-chiral topological orders are algebraically characterized by unitary modular tensor categories, which can be viewed as representation categories of the quantum double of a weak Hopf algebra. In this talk, I will discuss how to reconstruct the underlying weak Hopf algebra of a given topological phase within the string-net lattice model framework. Bulk, domain wall, and boundary tube algebras are explicitly shown to be weak Hopf algebras, whose representations correspond to topological excitations in the bulk, on domain walls, and along boundaries, respectively. I will further introduce a generalization of the Drinfeld quantum double to quantum N-tuple algebras, constructed via the gluing operation of boundary tubes. Finally, I will demonstrate how domain wall and boundary defects can be systematically characterized by generalized tube algebras formulated as comodule algebras. The notions of Drinfeld doubles and N-tuple algebras are naturally extendable to this generalized setting as well.