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.

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。回想一下，测量对称性的数学对象称为``组''，他们的研究被称为````组理论'''。组的经典示例是旋转或翻译（连续组）的示例和正方形或雪花的对称性（离散组）。 20世纪中叶，代数群体的诞生，捕捉连续群体（所谓的谎言群体）的精神的物体和离散的群体的诞生，但更普遍。在随后几十年的过程中，代数群体的理论已被用来对代数的几个关键领域和数字理论进行统一处理，包括二次形式的理论，中央简单代数，代数，具有相关性和一些非缔合性代数。