Computing with Lie groups and algebras: nilpotent orbits and applications

使用李群和代数进行计算：幂零轨道和应用

• 批准号: DP190100317
• 负责人: Prof Dr Heiko Dietrich
• 金额: $ 22.97万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-04-01 至 2023-01-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP190100317
• 关键词: Computing; Lie; groups; algebras; nilpotent

This project aims to advance knowledge of an important class of Lie algebras, for which recent work has shown that a deeper mathematical theory, and better computational tools are required. Lie theory is a mathematical area with rich applications in the physical sciences. Expected outcomes from this project include the first systematic treatment of these algebras, new powerful algorithms to compute with them, and explicit nilpotent orbit classifications that will solve open problems in black hole theory. This should significantly enhance fundamental mathematical research and the Lie functionality of leading computer algebra systems, and is expected to strengthen international linkages.

该项目旨在推进一类重要的李代数的知识，最近的工作表明，需要更深入的数学理论和更好的计算工具。李理论是一个数学领域，在物理科学中有着丰富的应用。该项目的预期成果包括首次系统地处理这些代数，使用它们进行计算的新的强大算法，以及明确的幂零轨道分类，这些分类将解决黑洞理论中的开放问题。这将大大加强基础数学研究和领先的计算机代数系统的Lie功能，并有望加强国际联系。