The structure of a Lie algebra attached to a unit form
The structure of a Lie algebra attached to a unit form

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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

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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