Mathematical Sciences: Geometries and Groups

数学科学：几何与群

• 批准号: 9204306
• 负责人: Ernest Shult
• 金额: $ 6.69万
• 依托单位: Kansas State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1994-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204306&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometries; Groups

This research is concerned with showing that hyperplanes of the major embeddable Lie incidence geometries all arise from embeddings. The cases that remain are dual polar spaces, geometries associated with exceptional Lie groups, and certain exceptional fields for the half-spin geometries. A class of geometries crucial to forming general theorems about Veldkamp spaces will also be considered. The principal investigator will continue work on ım!-ovoids, which are generalizations of both ovoids and spreads of polar spaces. The research in this project involves the interplay between finite dimensional geometry and the actions of groups of transformations on these geometries. This work has implications for the structure of finite groups, for algebraic coding theory, and for finite geometry.

这项研究的目的是表明主要可嵌入李重射几何形状的超平面都来自嵌入。 剩下的情况是双极空间、与特殊李群相关的几何结构以及半自旋几何结构的某些特殊场。 还将考虑对形成有关 Veldkamp 空间的一般定理至关重要的一类几何形状。 首席研究员将继续研究 Im!-ovoids，这是卵形体和极地空间扩展的概括。 该项目的研究涉及有限维几何与这些几何上的变换组的作用之间的相互作用。 这项工作对有限群的结构、代数编码理论和有限几何都有影响。