Extended affine Lie algebras, groups and representation theory

扩展仿射李代数、群和表示论

• 批准号: 8836-2011
• 负责人: Neher, Erhard
• 金额: $ 1.09万
• 依托单位: University of Ottawa
• 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=508561
• 关键词: Extended; affine; Lie; algebras; groups

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.

自19世纪以来，群的数学概念一直是数学家用来描述对称性的最基本的抽象结构之一。数学家们已经发展出了一种复杂的群理论，其应用越来越广泛。数学内外的群体应用是一个了不起的成功故事。最重要的一类群起源于挪威数学家Sophus Lie（1842- 1899）的基本工作。这些所谓的李群和它们的代数类似物，代数群的区别在于，人们可以将另一种数学结构，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。我的研究涉及某些类型的李代数和一些相关的结构。