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，以及它在自然界中如何以及为何出现，对于数学和物理学都很重要。在我的工作中，最好的例子可以在代数群和物理学之间的联系中找到，这些联系以仿射 Kac-Moody Lie 代数作为共同的桥梁。测量对称性的数学对象称为群。李群以挪威数学家 Sophus Lie 的名字命名，他在 19 世纪末发现并首次研究了这些物体，李群作为许多物理学理论的基本对称性自然而然地出现。 20 世纪中叶见证了代数群的诞生，这些对象体现了李群的精神，但也更加普遍。该研究项目的重点是了解代数群本身的本质及其在数学和物理学多个领域的应用。