Extended affine Lie algebras, groups and representation theory

自19世纪以来，群的数学概念一直是数学家用来描述对称的最基本的抽象结构之一，在许多不同的化身中，例如在科学和工程中。数学家们已经发展出一套复杂的群理论，具有越来越深刻的应用。数学内外群体的应用是一个非凡的成功故事。最重要的群类型源于挪威数学家Sophus Lie（1842- 1899）的基础性工作。这些所谓的李群和它们的代数类似物，即代数群，其区别在于人们可以将另一种数学结构，即李代数，与它们联系起来。粗略地说，李代数是相应群的一阶近似。我的研究是关于某些类型的李代数和一些相关的结构。

Since the 19th century the mathematical concept of a group has been one of the most basic abstract structures used by mathematicians to describe symmetry arising in many different incarnations, e.g. in science and engineering. Mathematicians have developed a sophisticated theory for groups with more and more profound applications. The applications of groups within and outside of mathematics have been a remarkable success story. The most important type of groups originates from the fundamental work of the Norwegian mathematician Sophus Lie (1842--1899). These so-called Lie groups and their algebraic analogues, the algebraic groups, are distinguished by the fact that one can associate another mathematical structure, a Lie algebra, to them. Roughly speaking, Lie algebras are first order approximations of the corresponding groups. My research is concerned with certain types of Lie algebras and some related structures.