Mathematical Sciences: Group Theory and Buildings

数学科学：群论和建筑

• 批准号: 9208692
• 负责人: Mark Ronan
• 金额: $ 7.85万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208692&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Group; Theory; Buildings

This research is concerned with twin buildings and Kac-Moody groups. The main thrust of the work is towards a classification of twin buildings of rank at least three, and the groups of Kac-Moody type which operate on them. The principal investigator will also study local-global properties of affine buildings and the global structure of hyperbolic buildings. The research supported is in a crucial area where several parts of mathematics intersect. This project endeavors to classify certain finite groups by using finite geometry and combinatorics. The geometric connection to the theory of reductive algebraic groups and Kac-Moody groups is important for the study of finite simple groups.

这项研究是关于双子楼和卡克-穆迪集团的。这项工作的主旨是对至少三级的孪生建筑以及在其上运作的Kac-Moody类型的群进行分类。首席研究员还将研究仿射建筑的局部-全局性质和双曲建筑的全局结构。所支持的研究是在数学的几个部分交叉的关键领域。这个项目致力于利用有限几何和组合学对某些有限群进行分类。与约化代数群和Kac-Moody群理论的几何联系对于有限单群的研究是重要的。