Mathematical Sciences: Group Theory and Combinatorics

数学科学：群论和组合学

• 批准号: 8704562
• 负责人: John Conway
• 金额: $ 6.14万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1988-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8704562&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Group; Theory; Combinatorics

This research is concerned with understanding the so-called Monster Group. There are three directions which the principal investigator will consider. One is to consider the relations between the group-characters of the Monster and certain classical modular forms. The second is the constructions of the group in 198684-dimension space. the third is the representation of the group in terms of hyperbolic reflections. This research is in the general area of finite group theory. It is concerned with studying a particular group called the Monster Group. This group is not well understood but has a very rich structure. At present calculations in the group are difficult, but whenever they have been performed successfully, wonderful and simple patterns have emerged. There are deep connections with other branches of mathematics and it seems quite likely that there are equally fundamental connections with theoretical physics.

这项研究旨在了解所谓的怪物群体。 首席研究员将考虑三个方向。 一是考虑怪物的群体特征与某些经典模块形式之间的关系。 二是群在198684维空间的构建。 第三个是用双曲反射来表示群。 这项研究属于有限群理论的一般领域。 它与研究一个称为“怪物群”的特定群体有关。 这个群体不太为人所知，但结构非常丰富。 目前小组中的计算很困难，但每当成功执行时，就会出现奇妙而简单的模式。 它与数学的其他分支有着深厚的联系，而且似乎很可能与理论物理学也有着同样基本的联系。