半单李代数的对偶根系  

Dual Root System of Semisimple Lie Algebras

作　　者：齐秀文 QI Xiu-wen(College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, Chin)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《伊犁师范学院学报（自然科学版）》2017年第3期19-22,共4页Journal of Yili Normal University：Natural Science Edition

摘　　要：半单李代数是目前研究很彻底的一种李代数,而根系是研究李代数结构及其表示的重要工具,是李代数研究的核心内容之一.许多关于李代数的著作及文献中经常只讨论根系,而对偶根系只限于简单提及,不详细讨论.首先给出李代数的对偶根系的公理形式,然后讨论在半单李代数情形下对偶根系的一个优越性质.Semisimple Lie algebra is one of the most thoroughly studied kind of Lie algebra, and the root system is one of the important tool in the study of Lie algebras and their representations, and so it is one of the central object in the study of Lie algebras. In the literature on the Lie algebras, only root system is studied, but the dual root system is only mentioned. In this paper, first, we prove the axiomatic form of the dual root system, then apply it to the semisimple Lie algebras to explain the importance of the dual root system.

关 键 词：半单李代数 KILLING 根系 对偶根系 

分 类 号：O152.5[理学—数学]