Infinite-dimensional Lie algebras and their applications

无限维李代数及其应用

• 批准号: RGPIN-2019-06170
• 负责人: Billig, Yuly
• 金额: $ 1.38万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=677013
• 关键词: Infinite; dimensional; Lie; algebras; their

Lie theory, named after a Norwegian mathematician Sophus Lie, is a vibrant area of modern mathematics with applications ranging from string theory to satellite control and quantum computing.******We propose to develop representation theory of Lie algebras of vector fields on affine algebraic varieties. This theory will combine the features of commutative and non-commutative algebra. Building on the recent advances we made in representation theory of vector fields on a torus, we would like to prove a classification theorem in the setting of an arbitrary smooth algebraic variety.******A part of this proposal is of a more applied nature. We propose to solve several optimal control problems on unitary groups. Solving these problems will have ramifications for quantum control and quantum computing.**

李理论以挪威数学家索夫斯·李命名，是现代数学中一个充满活力的领域，其应用范围从弦理论到卫星控制和量子计算。******我们提出在仿射代数变体上发展向量场李代数的表示理论。这个理论结合了交换代数和非交换代数的特点。基于我们在环面上向量场表示理论方面的最新进展，我们想要证明一个在任意光滑代数变集下的分类定理。******这个建议的一部分是更实用的。我们提出解决几个酉群上的最优控制问题。解决这些问题将对量子控制和量子计算产生影响