Infinite-dimensional Lie algebras in string theory

点击翻译按钮获取中文摘要

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.