RESEARCH ARTICLE

A class of simple Lie algebras attached to unit forms

  • Jinjing CHEN 1 ,
  • Zhengxin CHEN , 2
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  • 1. School of Mathematical Sciences, Xiamen University, Xiamen 361000, China
  • 2. School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou 350117, China

Received date: 22 Feb 2016

Accepted date: 17 Nov 2016

Published date: 06 Jul 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let n≥3.The complex Lie algebra, which is attached to a unit form q(x1,x2,,xn)=i=1nxi2+1ijn(1)jixixj 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.

Cite this article

Jinjing CHEN , Zhengxin CHEN . A class of simple Lie algebras attached to unit forms[J]. Frontiers of Mathematics in China, 2017 , 12(4) : 787 -803 . DOI: 10.1007/s11464-016-0616-x

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