李三系的表示理论

Pub Date : 2022-01-01 DOI:10.12988/ija.2022.91720

A. Alshahrani

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引用次数: 1

摘要

本文研究了李代数、李三重系和乔丹三重系的某些方面。总结了李代数和李三重系的普适包络代数的最新研究成果。特别地，我们研究了一个卡西米尔元作为普适包络代数的中心元。利用这个元，我们刻画了二次李三元系统中的半简单李三元系统。我们用代数和李代数定义了Jordan的三重系统关系。最后，我们对上述的一些定理、例子和事实进行了证明。数学学科分类:17C50、17B60、17B20、17B05

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On representation theory of Lie triple systems

The present work concerns certain aspects of Lie algebras, Lie triple systems and Jordan triple systems. We summarize the latest results on the universal enveloping algebras of Lie algebras and Lie triple systems. In particular, we study a Casimir element as the element in the center of the universal enveloping algebras. Using this element, we characterize the semi-simple Lie triple systems among the quadratic Lie triple systems. We define Jordan’s triple systems relationship with algebras and Lie algebras. Finally, we prove some theorems, examples and facts on all of the above. Mathematics Subject Classification: 17C50, 17B60, 17B20, 17B05

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