Infinite-dimensional Lie theory and its applications

无限维李理论及其应用

• 批准号: RGPIN-2014-05851
• 负责人: Billig, Yuly
• 金额: $ 1.31万
• 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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=611883
• 关键词: Infinite; dimensional; Lie; theory; its

Lie theory is named after its founder, 19th century Norwegian mathematician Sophus Lie. This theory is used to describe continuous symmetries of mathematical and physical objects. In particular, control of quantum systems is based on Lie theory. For basic quantum models, like the spin of an electron, the number of symmetries is infinite, but the dimension of the group of symmetries is still finite. In string theory, on the other hand, the group of symmetries is infinite-dimensional. This proposal is aimed at the advancement of the Lie theory with a view towards possible applications to quantum computing and string theory.

Lie理论是以其创始人、世纪挪威数学家Sophus Lie命名的。这个理论被用来描述数学和物理对象的连续对称性。特别是，量子系统的控制是基于李理论。对于基本的量子模型，比如电子的自旋，对称的数量是无限的，但是对称群的维数仍然是有限的。另一方面，在弦论中，对称群是无限维的。这个提议的目的是为了推进李理论，以期在量子计算和弦理论中有可能的应用。