Fusing Binary Interface Defects in Topological Phases: The $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$ case

Domain walls in topological phases and the Brauer-Picard ring for $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$

We show how to calculate the relative tensor product of bimodule categories (not necessarily invertible) using ladder string diagrams. As an illustrative example, we compute the Brauer-Picard ring for the fusion category $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$. Moreover, we provide a physical interpretation of all indecomposable bimodule categories in terms of domain walls in the associated topological phase. We show how this interpretation can be used to compute the Brauer-Picard ring from a physical perspective.

Computing Defects Associated to Bounded Domain Wall Structures: The $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$ Case

A domain wall structure consists of a planar graph with faces labeled by fusion categories/topological phases. Edges are labeled by bimodules/domain walls. When the vertices are labeled by point defects we get a compound defect. We present an algorithm, called the domain wall structure algorithm, for computing the compound defect. We apply this algorithm to show that the \emph{bimodule associator}, related to the $O_3$ obstruction of [Etingof et al., Quantum Topol. 1, 209 (2010), arXiv:0909.3140], is trivial for all domain walls of $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$. In the language …

模偶数群的模Z₂交叉Tambara-Yamagami-like范畴

Modular $\mathbb{Z}_2$-Crossed Tambara-Yamagami-like Categories for Even Groups

本文构建了非退化braided Z₂交叉张量范畴，扩展了Tambara-Yamagami范畴，允许Γ群有偶阶且非平凡部分包含多个单对象。

双交叉积与融合范畴的交叉扩张之间的关系

Relation between bicrossed products and crossed extensions of fusion categories

本文证明 Natale 定义的交叉扩张均可通过对偶的双交叉积恢复，并由此说明点融合范畴与融合范畴间的精确分解都能实现为双交叉积。