Mathematical Sciences: Crossed Products over Rational Function Fields

数学科学：有理函数域上的叉积

• 批准号: 9024863
• 负责人: Burton Fein
• 金额: $ 11.4万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9024863&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Crossed; Products; over

This project is concerned with problems in ring theory and deals with questions about the maximal subfields of finite dimensional division algebras. The principal investigator will consider the following two questions: (1) given a finite algebraic extension L of a field K, does there exist a finite dimensional division algebra with center K containing L as a maximal subfield?, and (2) given a finite group G which occurs as a Galois group over K, does there exist a Galois extension L of K with the Galois group of L/K isomorphic to G and a factor set f mapping GXG into L* such that the crossed product algebra (L/K,f) is a division ring? The research supported in this project is in the general area of ring theory. The principal investigator will study how one central simple algebra can contain another. This work draws on some deep results in group theory and will shed light on various questions in algebra and number theory.

该项目涉及环理论中的问题，并处理有关有限维除代数的最大子域的问题。 主要研究者将考虑以下两个问题：（1）给定域 K 的有限代数扩张 L，是否存在以 K 为最大子域且包含 L 的有限维除代数？（2）给定有限群 G，它作为 K 上的伽罗瓦群出现，是否存在 K 的伽罗瓦扩张 L，其中 L/K 同构于 G 的伽罗瓦群和因子集 f 将 GXG 映射到 L* 使得叉积代数 (L/K,f) 是除环？ 该项目支持的研究属于环理论的一般领域。 首席研究员将研究一个中心简单代数如何包含另一个中心简单代数。 这项工作借鉴了群论的一些深刻成果，并将阐明代数和数论中的各种问题。