# Frontiers of Mathematics in China

 Front. Math. China    2017, Vol. 12 Issue (4) : 787-803     DOI: 10.1007/s11464-016-0616-x
 RESEARCH ARTICLE |
A class of simple Lie algebras attached to unit forms
Jinjing CHEN1, Zhengxin CHEN2()
1. School of Mathematical Sciences, Xiamen University, Xiamen 361000, China
2. School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou 350117, China
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 Abstract Let n≥3.The complex Lie algebra, which is attached to a unit form $q(x1,x2,…,xn)=∑i=1nxi2+∑1≤i≤j≤n(−1)j−ixixj$ and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type $An$,and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra. Corresponding Authors: Zhengxin CHEN Issue Date: 06 July 2017
 Cite this article: Jinjing CHEN,Zhengxin CHEN. A class of simple Lie algebras attached to unit forms[J]. Front. Math. China, 2017, 12(4): 787-803. URL: http://journal.hep.com.cn/fmc/EN/10.1007/s11464-016-0616-x http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/787