Computing with matrix groups and Lie algebras: new concepts and applications

使用矩阵群和李代数进行计算：新概念和应用

• 批准号: DE140100088
• 负责人: Prof Dr Heiko Dietrich
• 金额: $ 26.47万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-02-01 至 2017-02-01
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE140100088
• 关键词: Computing; matrix; groups; Lie; algebras

Computational algebra combines symbolic computation and pure research in algebra, and is concerned with the design of algorithms for solving mathematical problems endowed with algebraic structure. Matrix groups and Lie algebras are prominent algebraic objects describing the natural concept of symmetry. Despite being very common and important in science, there is a paucity of algorithms to study their structure. This project will develop deep new mathematical theories for computing with these objects, leading to ground-breaking advances in computational algebra, and providing powerful tools facilitating new research, including in other sciences. The new functionality will be used to solve two classification problems in group and Lie theory.

计算代数结合了符号计算和代数的纯研究，并关注解决具有代数结构的数学问题的算法设计。矩阵群和李代数是描述对称性的自然概念的突出代数对象。尽管在科学中非常常见和重要，但研究其结构的算法却很少。该项目将为这些对象的计算开发新的数学理论，导致计算代数的突破性进展，并提供强大的工具，促进新的研究，包括在其他科学。新的功能将被用来解决两个分类问题的群和李理论。