Characterizing algebraic groups via maximal tori

通过最大环面表征代数群

• 批准号: RGPIN-2017-05749
• 负责人: Chernousov, Vladimir
• 金额: $ 1.46万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 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=635450
• 关键词: Characterizing; algebraic; groups; via; maximal

Understanding symmetry, and how and why it arises in nature, is important in both Mathematics and Physics. Recall that the mathematical objects that measure symmetry are called ``groups'' and their study is known as ``group theory''. Classical examples of groups are those of rotations or translations (continuous groups) and the symmetry of a square or a snowflake (discrete groups). The mid 20th century saw the birth of Algebraic Groups, objects that capture the spirit of continuous groups (the so-called Lie groups) and discrete groups, but that are much more universal. Over the course of subsequent decades the theory of algebraic groups has been used to give a unified treatment of several key areas of algebra and number theory, including the theories of quadratic forms, central simple algebras, algebras with involution and some non-associative algebras.

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。回想一下，测量对称性的数学对象被称为“群”，他们的研究被称为“群论”。群的经典例子是旋转或平移（连续群）和正方形或雪花对称（离散群）。世纪中期，代数群诞生了，代数群是一种具有连续群（所谓的李群）和离散群的精神的对象，但它更具有普遍性。在随后的几十年中，代数群理论被用来统一处理代数和数论的几个关键领域，包括二次型理论、中心单代数、对合代数和一些非结合代数。