Infinite-dimensional Lie algebras in string theory

弦理论中的无限维李代数

• 批准号: 243643317
• 负责人: Professor Dr. Nils R. Scheithauer
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/243643317?language=en
• 关键词: Infinite; dimensional; Lie; algebras; string

Affine Kac-Moody algebras are affinizations of the finite-dimensional simple Lie algebras. They have various applications in mathematics and physics, e.g. in geometry and string theory. It has turned out that there is another class of infinite-dimensional Lie algebras which has similarly nice properties. These are the generalized Kac-Moody algebras whose denominator functions are automorphic forms of singular weight on orthogonal groups. These Lie algebras can be classified. It is believed that they describe strings moving on suitable orbifolds. The objective of this project is to give a proof of this conjecture.

仿射Kac-Moody代数是有限维单李代数的仿射化。它们在数学和物理学中有各种应用，例如几何学和弦理论。事实证明，还有另一类无限维李代数具有类似的好性质。这些是广义Kac-Moody代数，其分母函数是正交群上奇异权的自守形式。这些李代数可以分类。人们相信它们描述了在合适的轨道上运动的弦。这个项目的目标是证明这个猜想。