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: 2021
• 资助国家: 加拿大
• 起止时间: 2021-01-01 至 2022-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=738756
• 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.

Lie理论以挪威数学家Sophus Lie的名字命名，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。本文提出了仿射代数簇上向量场李代数的表示理论。这个理论将联合收割机结合交换代数和非交换代数的特点。基于最近的进展，我们在表示理论的向量场的环面，我们想证明一个分类定理的设置任意光滑代数簇。这一建议的一部分具有更实用的性质。我们提出解决酉群上的几个最优控制问题。解决这些问题将对量子控制和量子计算产生影响。