Geometric Methods in Group Theory

群论中的几何方法

• 批准号: 9401627
• 负责人: Hyman Bass
• 金额: $ 10.43万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401627&HistoricalAwards=false
• 关键词: Geometric; Methods; Group; Theory

9401627 Bass This award supports research on a number of questions in group theory using geometric methods. The principal investigator will work on linearizing flat families of reductive group representations; renormalization in interval dynamics and automorphism groups of rooted trees; calculating the stabilizer, in the outer automorphism group, of the hyperbolic length function of a simplicial tree action; developing the theory of non-uniform tree lattices; and several topics in the representation theory of finitely generated groups. A lattice is a set of objects together with an order on these objects such that any pair of objects has a greatest lower bound and a least upper bound. Lattices have shown to be quite useful in the study of Lie groups. In a similar spirit this project will explore lattices in the automorphism group of certain trees. This work is of interest to many different areas of mathematics. It also has potential applications in information theory.

9401627 低音 该奖项支持使用几何方法对群论中的一些问题进行研究。 主要研究人员将致力于线性化平面家庭的还原群表示;重整区间动力学和自同构群的根树;计算稳定剂，在外部自同构群，双曲长度函数的单纯树行动;发展理论的非均匀树格;和几个主题的代表性理论的生成群。 格是一组对象以及这些对象上的顺序，使得任何一对对象都具有最大下界和最小上界。 格在李群的研究中已被证明是非常有用的。 本着类似的精神，这个项目将探索某些树的自同构群中的格。 这项工作是感兴趣的许多不同领域的数学。 它在信息论中也有潜在的应用。