Mathematical Sciences: Minimal Embeddings in Central Simple Algebras

数学科学：中心简单代数的最小嵌入

• 批准号: 8801051
• 负责人: Murray Schacher
• 金额: $ 16.85万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801051&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Minimal; Embeddings; Central

This project is concerned with the structure of central simple algebras and the ways in which they combine to form Brauer groups. The principal investigator will study central simple algebras in order to explore how one of them can contain another. An ultimate goal is to explore how semisimple algebras, which are built from central simple algebras, can be inserted into central simple algebras over other fields. Solutions to these problems will have applications in the theory of finite groups. The research supported concerns the study of the Brauer group of a field. This group is an invariant that helps to explain the structure of the algebras over fields that occur as subalgebras of rings of matrices or linear transformations. This work has shed light on the structure of finite dimensional division rings and has potential applications to the theory of finite groups.

本项目涉及中央 简单代数和它们联合收割机形成布劳尔的方法 组 主要研究者将研究中心简单 代数，以探索它们中的一个如何包含另一个。 最终的目标是探索半单代数， 由中心单代数建立，可以插入到中心 其他领域上的简单代数 这些问题的解决方案 将在有限群理论中得到应用。 这项研究支持的是对布劳尔的研究， 一个领域的一组。这个群是一个不变量， 解释域上代数的结构， 矩阵环或线性变换的子代数。这 工作揭示了有限维的结构， 除环，并有潜在的应用理论， 有限群