The structure of a Lie algebra attached to a unit form
The structure of a Lie algebra attached to a unit form
投稿时间:2017-11-04  修订日期:2018-08-12
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中文关键词:  
英文关键词:Nakayama algebras, finite dimensional simple Lie algebras, Ringel-Hall Lie algebras
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作者单位E-mail
于亚龙 福建师范大学 1670240028@qq.com 
陈正新 福建师范大学 czxing@163.com 
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中文摘要:
      
英文摘要:
      Let $n\geq 4$. The complex Lie algebra, which is attached to a unit form $\mathfrak{q}(x_1,x_2,\cdots, x_n)=\sum\limits_{i=1}^nx_i^2-(\sum\limits_{i=1}^{n-1}x_ix_{i+1})+x_1x_n $ and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type $\mathbb{D}_n$, 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.
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