Higher Representation Theory

更高表征理论

• 批准号: DE150101415
• 负责人: Dr Peter McNamara
• 金额: $ 24.84万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-02-02 至 2023-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE150101415
• 关键词: Higher; Representation; Theory

Representation theory is a field of mathematics with applications across the breadth of mathematical study in fields as diverse as number theory and physics. The study of higher (or categorical) representation theory is a modern set of tools that provides new insights into representation theoretic phenomena. This project aims to study categorified quantum groups and, in particular, the categorifications provided by diagrammatic algebras. The project aims to further develop the theory of Khovanov-Lauda-Rouquier (KLR) algebras, providing important foundational results for future research to build upon.

表示论是一个数学领域，在数学研究的各个领域都有应用，从数论到物理学都有。对更高(或范畴)表征理论的研究是一套现代工具，它为表征理论现象提供了新的见解。这个项目的目的是研究范畴化量子群，特别是由图代数提供的范畴化。该项目旨在进一步发展Klovov-Lauda-Rouquier(KLR)代数理论，为今后的研究提供重要的基础性成果。