The Structure of a Lie Algebra Attached to a Unit Form  

作　　者：Yalong YU Zhengxin CHEN 

机构地区：[1]College of Mathematics and Informatics, Fujian Normal University

出　　处：《Journal of Mathematical Research with Applications》2019年第5期469-488,共20页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11571360);the Natural Science Foundation of Fujian Province(Grant Nos.2016J01006; JZ160427)

摘　　要：Let n≥4. The complex Lie algebra, which is attached to the unit form q(x1,x2,…xn)=Σ^n i=1 x2i -(Σn-1 i=1 xixi+1)+x1xn and defned by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type Dn, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra.Let n ≥ 4. The complex Lie algebra, which is attached to the unit form q(x1, x2,..., xn)■ and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type Dn, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra.

关 键 词：Nakayama ALGEBRAS finite DIMENSIONAL simple LIE ALGEBRAS Ringel-Hall LIE ALGEBRAS 

分 类 号：O1[理学—数学]