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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759234
• 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.

以挪威数学家索斯（Sophus）谎言命名的谎言理论是现代数学的一个充满活力的领域，其应用从字符串理论到卫星控制和量子计算。我们建议开发对载体代数品种的载体场谎言代数的表示理论。该理论将结合交换性和非共同代数的特征。在我们在圆环上代表矢量场中取得的最新进展为基础，我们希望在任意平滑代数变体的环境中证明分类定理。该提案的一部分具有更高的应用性质。我们建议解决统一组的几个最佳控制问题。解决这些问题将对量子控制和量子计算产生影响。