Mathematical Sciences: Sporadic Groups and Infinite Dimensional Groups

[304279] Griess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来联合所有零星的简单群。具体来说，首席研究员将研究与晶格相关的无限维群的一般结构。他将研究与李群相关的有限结构，并发展一类幂零2类群的自同构群的一般理论。他将进一步通过标记Coxeter-Dynkin图等数据对有限维单李群的有限子群进行分类。首席研究员还将研究一个新版本的月光舱。群是具有单一运算的代数结构。它出现在数学的许多领域，以及物理和化学。有限群的基本组成部分是有限单群。过去十年数学的主要成果之一是有限单群的分类，证明它需要1万到1.5万页的期刊。本研究旨在将此分类应用于任意有限群的研究。＊＊＊

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. ***