Mathematical Sciences: Nonassociative Algebras

数学科学：非结合代数

• 批准号: 8800691
• 负责人: J. Marshall Osborn
• 金额: $ 14.7万
• 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: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8800691&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Nonassociative; Algebras

This project is concerned with research on simple Lie algebras of prime characteristic. The principal investigators have made significant progress in analyzing the structure of 1-sections of simple algebras and have begun studying 2-sections. The determination of the 1- and 2-sections was an essential step in the classification of the restricted simple Lie algebras and it is believed to be an essential step in the classification of the nonrestricted algebras as well. The principal investigators will do an extensive investigation of the structure of 2-sections in simple prime characteristic algebras and will apply the information obtained to the classification of the simple nonrestricted Lie algebras. Work will also be done on bringing over certain stability results to the affine Kac-Moody setting. The characterization of finite dimensional Lie algebras over an algebraically closed field of prime characteristic has a long history and is one of the important outstanding problems in mathematics. This project supports work on the remaining cases of this characterization.

本课题是关于简单Lie的研究 素特征的代数 主要研究者 在分析结构方面取得了重大进展， 1-简单代数的部分，并开始研究 两部分。1段和2段的确定是一个复杂的过程。 限制单纯形分类的基本步骤 李代数，它被认为是一个重要的一步， 非限制代数的分类。的 主要调查人员将进行广泛的调查， 单素特征2-截线结构 代数，并将获得的信息应用于 简单非限制李代数的分类。工作 也将在带来一定的稳定性结果， 仿射Kac-Moody设置 有限维李代数的刻画 在素特征的代数闭域上， 历史悠久，是我国社会主义现代化建设中的重要突出问题之一 在数学上。该项目支持在剩余的 这种特征的案例。