Mathematical Sciences: Nonassociative Algebras

本课题主要研究具有素数特征的单李代数。主要研究者在分析简单代数的1-节的结构方面取得了重大进展，并开始研究2-节。1-截口和2-截口的确定是限制单李代数分类的一个重要步骤，也是非限制单李代数分类的一个重要步骤。主要研究人员将对简单素数特征代数的两节结构进行广泛的研究，并将所获得的信息应用于简单非限制李代数的分类。还将努力将某些稳定性结果带到仿射Kac-Moody设置中。具有素数特征的代数闭域上的有限维李代数的刻画由来已久，是数学中的一个重要的突出问题。该项目支持关于这一定性的其余案例的工作。

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.