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: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=522933
• 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.

谎言理论以其创始人19世纪的挪威数学家Sophus谎言命名。该理论用于描述数学和物理对象的连续对称性。爱因斯坦（Einstein）采用了这一理论，从一个关于时空的对称结构的一个假设中得出了他的特殊相对论。在此示例中，对称的数量是无限的，但是对称组的维度仍然有限​​。另一方面，在弦理论中，对称性是无限维度的。该提议旨在提高无限维谎言理论，并观察到弦理论的可能应用。