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.

了解对称性，以及它在自然界中的出现以及为什么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体和物理学之间的连接中找到，这些群体将仿射kac-moody lie代数作为公共桥梁。测量对称性的数学对象称为组。以挪威数学家索斯（Sophus）谎言命名的谎言团体在19世纪末发现并首次研究了这些物体，自然而然地出现了许多物理学理论的基础对称性。 20世纪中叶看到了代数群体的诞生，捕捉谎言群体精神的物体却更加普遍。研究项目集中在理解代数群体本身的本质以及它们在数学领域以及物理学领域的应用。