Computing with Lie groups and algebras: nilpotent orbits and applications

该项目旨在提高对一类重要李代数的认识，最近的工作表明，这需要更深入的数学理论和更好的计算工具。李论是一个在物理科学中有着丰富应用的数学领域。这个项目的预期成果包括对这些代数的第一次系统处理，用它们计算的新的强大算法，以及将解决黑洞理论中开放问题的显式幂零轨道分类。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。

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.