Algebra

代数

• 批准号: 1000219864-2010
• 负责人: Chernousov, Vladimir
• 金额: $ 14.57万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Canada Research Chairs
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=642761
• 关键词: Algebra

Understanding symmetry, and how and why it arises in nature, is important in both Mathematics and Physics. Within my work the best examples are to be found in the connections between Algebraic Groups and Physics that have the Affine Kac-Moody Lie algebras as a common bridge. The mathematical objects that measure symmetry are called Groups. Lie groups, named after the Norwegian mathematician Sophus Lie who discovered and first studied these objects late in the 19th century, arise naturally as the underlying symmetry of many theories in Physics. The mid 20th century saw the birth of Algebraic Groups, objects that capture the spirit of Lie groups yet are much more universal. The research project centres on understanding the very nature of algebraic groups themselves, and their applications to several areas of Mathematics, as well as Physics.

理解对称性，以及它如何以及为什么在自然界中出现，在数学和物理学中都很重要。在我的工作中，最好的例子是在代数群和物理学之间的联系中找到的，这些联系以仿射卡茨-穆迪李代数为共同的桥梁。测量对称性的数学对象称为群。李群是以挪威数学家索菲斯·李（Sophus Lie）的名字命名的，他在世纪末发现并首次研究了这些物体，李群作为物理学中许多理论的基础对称性而自然出现。世纪中期，代数群诞生了，它体现了李群的精神，但更具有普遍性。该研究项目的重点是理解代数群本身的性质，以及它们在数学和物理学的几个领域的应用。