Quadratic fusion categories: A frontier in subfactor theory

二次融合类别：子因子理论的前沿

• 批准号: DP170103265
• 负责人: Dr Pinhas Grossman
• 金额: $ 21.72万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170103265
• 关键词: Quadratic; fusion; categories; frontier; subfactor

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.

本计画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对称性的数学结构。这些结构出现在算子代数和共形场论的数学模型中子因子的不变量。二次融合范畴包含了大多数已知的子因子，这些子因子不是来自有限群或量子群，而是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，该项目将推进子因子理论并为共形场论提供新模型。这些领域的进展将应用于新兴的量子计算技术。