Mathematical Sciences: Topological Methods in Algebraic Transformation Groups

数学科学：代数变换群中的拓扑方法

• 批准号: 9003288
• 负责人: Ted Petrie
• 金额: $ 17.41万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1994-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003288&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topological; Methods; Algebraic

This project treats algebraic (and analytic) actions on affine varieties from the viewpoint of smooth (differentiable) transformation groups. The subject of smooth transformation groups has been strongly influenced by the following two central problems: LINEARITY PROBLEM. Which groups act nonlinearly on affine space of some dimension? (An action is linear if it is conjugate to an action defined by a representation of the group.) FIXED POINT PROBLEM. Which groups act without fixed points on affine space of some dimension? The tools used to settle these problems and the further problems they generated have been important themes in the field of smooth transformation groups. During the last few years researchers from algebraic transformation groups as well as those from smooth transformation groups have recognized the importance of these two questions in the algebraic category, and in that case the groups dealt with should be reductive (which includes as a special case the finite groups). Petrie will continue his work in this direction, bringing topological methods to bear on algebraic questions.

这个项目处理代数（和分析）的行动 从光滑（可微）观点看仿射簇 变换群 光滑变换的主题 受以下两个核心因素的影响， 问题：线性问题。 哪些群体非线性作用于 某维仿射空间 (An如果它是线性的， （1）由一个群的表示所定义的作用的共轭。 不动点问题 哪些群体没有固定点， 某维仿射空间 用来解决这些问题的工具 问题及其产生的进一步问题， 平滑变换群领域的重要主题。 在过去的几年里，来自代数的研究人员 变换群以及平滑变换群 这两个问题的重要性， 代数范畴，在这种情况下， 应该是还原的（包括作为特殊情况的有限 组）。 皮特里将继续朝这个方向努力， 将拓扑方法应用于代数问题。