Mathematical Sciences: Sporadic Groups and Infinite Dimensional Groups

数学科学：零星群和无限维群

• 批准号: 9304279
• 负责人: Robert Griess
• 金额: $ 6万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9304279&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Sporadic; Groups; Infinite

9304279 Griess This award supports research aimed at developing a theory which will unite all the sporadic simple groups by means of infinite dimensional groups. Specifically, the principal investigator will investigator the general structure of infinite dimensional groups associated to lattices. He will study finite structures associated to Lie groups and develop a general theory of automorphism groups of a class of nilpotence class 2 groups. He will further classify finite subgroups of finite dimensional simple Lie groups by data such as labeled Coxeter-Dynkin diagrams. The principal investigator will also work on a new version of a moonshine module. A group is an algebraic structure with a single operation. It appears in many areas of mathematics, as well as, physics and chemistry. The fundamental building blocks of finite groups are finite simple groups. One of the major results in mathematics of the past decade is the classification of the finite simple groups, the proof of which would require 10,000 to 15,000 journal pages. This research is aimed at using this classification in the study of arbitrary finite groups. ***

小行星9304279 该奖项支持旨在发展一种理论的研究，该理论将通过无限维群将所有零星的简单群联合起来。 具体来说，首席研究员将研究与格相关联的无限维群的一般结构。 他将研究有限结构相关的李群和发展一般理论的自同构群的一类nilomentum类2组。 他将进一步分类有限子群的有限维简单李群的数据，如标记考克斯特-Dynkin图。 首席研究员还将致力于一个新版本的月光模块。 一个群是一个具有单一运算的代数结构。 它出现在数学、物理和化学的许多领域。 有限群的基本构造块是有限单群。 在过去的十年中，数学的主要成果之一是有限单群的分类，证明它需要10，000到15，000页的期刊。 本研究的目的是使用这种分类在任意有限群的研究。 ***