Quasi-hereditary categories in Lie theory

李理论中的准遗传范畴

• 批准号: DE170100623
• 负责人: A/Prof Kevin Coulembier
• 金额: $ 25.19万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-06-30 至 2021-06-29
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE170100623
• 关键词: Quasi; hereditary; categories; Lie; theory

This project aims to use diagram algebras and categorical representation theory to study fundamental open problems in the representation theory of Lie algebras and their generalisations. The concept of symmetry is omnipresent in science and culture. Its mathematical study leads to the notion of groups, algebras and their representation theory. Representation theory is applicable in many active research areas, including subatomic particle physics and quantum computing. Solutions to these problems could lead to better understanding of several categories of representations of Lie algebras, and create new research tools.

这个项目的目的是使用图代数和范畴表示理论来研究李代数的表示理论及其推广中的基本开放问题。对称的概念在科学和文化中无处不在。它的数学研究导致了群、代数及其表示论的概念。表示论适用于许多活跃的研究领域，包括亚原子粒子物理和量子计算。这些问题的解决方案可能会导致更好地理解李代数的几类表示，并创造新的研究工具。