The Congruence Subgroup Problem and Groups of Finite Representation Type

同余子群问题与有限表示型群

• 批准号: 9700474
• 负责人: Andrei Rapinchuk
• 金额: $ 4.99万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9700474&HistoricalAwards=false
• 关键词: Congruence; Subgroup; Problem; Groups; Finite

9700474 Rapinchuk This award provides funding for a continuing of the congruence subgroup problem for S-arithmetic subgroups of linear algebraic groups over number fields. The principal investigator will attempt to prove the centrality of the congruence kernel for some new classes of groups using a variety of techniques such as different boundedness conditions (bounded generation and similar properties), methods of representation theory (property (T) of Kazhdan), etc. He will also study the properties of groups having finite representation type and the representation varieties of some finitely generated groups. This research falls into the general mathematical field of Number Theory. Number Theory has its historical roots in the study of the whole numbers, addressing such questions as those dealing with the divisibility of one whole number by another. It is among the oldest branches of mathematics and was pursued for many centuries for purely aesthetic reasons. However, within the last half century it has become an indispensable tool in diverse applications in areas such as data transmission and processing, and communication systems.

这个奖项为数域上线性代数群的s -算术子群的同余子群问题的一个连续提供了资助。主要研究者将尝试使用不同有界条件（有界生成和相似性质）、表示理论方法（哈萨克丹性质(T)）等各种技术来证明一些新类群的同余核的中心性。他还将研究有限表示型群的性质和一些有限生成群的表示变化。本研究属于数论的一般数学领域。数论的历史根源在于对整数的研究，解决的问题是一个整数能被另一个整数整除的问题。它是数学中最古老的分支之一，人们为了纯粹的美学原因而追求了许多世纪。然而，在过去的半个世纪里，它已经成为数据传输和处理以及通信系统等各种应用领域不可或缺的工具。