We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is emphasized. Connections to two-dimensional conformal field theory are also presented. In particular, we discuss anyon condensation, gapped domain walls and matrix product operators in terms of operator algebras.

中文翻译：

---

二维拓扑顺序和算子代数

我们回顾了二维拓扑序的数学理论与算子代数之间的最新相互作用，特别是子因子的琼斯理论。强调了表示论在张量范畴方面的作用。还介绍了与二维共形场论的联系。特别是，我们根据算子代数讨论任意子凝聚、带隙畴壁和矩阵乘积算子。