Mathematical Sciences: Groups and Rings

数学科学：群和环

• 批准号: 8900405
• 负责人: I. Martin Isaacs
• 金额: $ 20.89万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-05-15 至 1993-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8900405&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Groups; Rings

This project is concerned with research in group theory and ring theory. One investigator will be working on character theory. In particular, he will examine M-groups, the properties of the set of irreducible character degrees of solvable groups and the interactions between characters and sets of primes in these groups. The other investigator will work on group rings, crossed products, Galois theory and enveloping rings. He will apply Delta-methods to restricted enveloping rings of infinite dimensional Lie algebras. He will also determine when such rings satisfy a polynomial identity. Furthermore he plans to work on computations of Grothendieck groups and Gelfand-Kirilov dimension. A group is an algebraic structure with one operation. A ring is an algebraic structure with two operations, addition and multiplication. It forms a group with respect to addition. These are basic abstract structures which occur in many settings in mathematics, chemistry and physics.

这个项目是关于群论和环理论的研究。一名调查员将研究性格理论。特别是，他将研究m群，可解群的不可约特征度集的性质，以及这些群中的特征与素数集之间的相互作用。另一名研究员将研究群环、交叉积、伽罗瓦理论和包络环。他将把delta方法应用于无限维李代数的受限包络环。他还将确定这些环何时满足多项式恒等式。此外，他计划研究Grothendieck群和Gelfand-Kirilov维数的计算。群是一种只有一次运算的代数结构。环是一种代数结构，有两种运算：加法和乘法。它就加法形成了一个群。这些是基本的抽象结构，在数学、化学和物理的许多场景中都会出现。