Quadratic fusion categories: A frontier in subfactor theory

本项目旨在研究二次融合范畴的量子对称性。融合范畴是推广有限群的对称性的数学结构。这些结构在算子代数和共形场理论的数学模型中作为子因子的不变量出现。二次融合范畴涵盖了大多数已知子因子，它们不是来自有限群或量子群，并形成了一个鲜为人知的广阔前沿。通过揭示二次融合范畴的对称性，该项目将推进次因子理论，并为保形场理论提供新的模型。这些领域的进展将应用于新兴的量子计算技术。

This project aims to investigate the quantum symmetries of the quadratic fusion categories. Fusion categories are mathematical structures that generalise the symmetries of finite groups. These structures arise as invariants of subfactors in operator algebras and in mathematical models of conformal field theory. The quadratic fusion categories encompass most known subfactors that do not come from finite or quantum groups and form a vast frontier about which little is known. By uncovering the symmetries of the quadratic fusion categories, the project will advance subfactor theory and provide new models for conformal field theory. Progress in these fields will have applications to the emerging technology of quantum computing.