Mathematical Sciences: Jordan Structure Theory

这个项目是关于约旦代数和三重系统的结构。首席研究员将扩展Zelmanov对Jordan结构的素双模分类。他将研究Clifford型质数Jordan三重系统的结构，并研究Glennie和Thedy的s-恒等式。此外，还考虑了Jordan和可选超代数对普通Jordan和可选超代数结构的影响。本研究涉及约当代数的研究。20世纪20年代，物理学家p·乔丹（P. Jordan）努力寻找量子力学形式主义的代数推广，由此产生了乔丹代数。这些结构与几个不同的数学领域有一些有趣的联系。

This project is concerned with the structure of Jordan algebras and triple systems. The principal investigator will extend Zelmanov's classification of prime bimodules for Jordan structures. He will study the structure of prime Jordan triple systems of Clifford type and investigate the s-identities of Glennie and Thedy. In addition, the influence of Jordan and alternative superalgebras on the structure of ordinary Jordan and alternative algebras will be considered. This research is concerned with the study of Jordan algebras. Jordan algebras arose in the 1920's through the efforts of the physicist P. Jordan to find an algebraic generalization of the formalism of quantum mechanics. These structures have some interesting connections with several different areas of mathematics.