Infinite-dimensional Lie algebras and their applications

无限维李代数及其应用

• 批准号: 183654-2009
• 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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503656
• 关键词: Infinite; dimensional; Lie; algebras; their

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. Applying this theory, Einstein derived his special relativity theory from a single postulate about the symmetry structure of the space-time. In this example, 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 infinite-dimensional Lie theory with a view on possible applications to string theory.

李理论以其创始人、19 世纪挪威数学家索菲斯·李 (Sophus Lie) 的名字命名。该理论用于描述数学和物理对象的连续对称性。应用这一理论，爱因斯坦从关于时空对称结构的单一假设中得出了他的狭义相对论。在这个例子中，对称性的数量是无限的，但是对称性群的维数仍然是有限的。另一方面，在弦理论中，对称群是无限维的。该提案旨在推进无限维李理论，并着眼于弦理论的可能应用。