A class of simple Lie algebras attached to unit forms |
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Authors: | Jinjing Chen Zhengxin Chen |
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Institution: | 1.School of Mathematical Sciences,Xiamen University,Xiamen,China;2.School of Mathematics and Computer Science & FJKLMAA,Fujian Normal University,Fuzhou,China |
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Abstract: | Let n ≥ 3. The complex Lie algebra, which is attached to a unit form q(x 1, x 2,..., x n) = \({\sum\nolimits_{i = 1}^n {x_i^2 + \sum\nolimits_{1 \leqslant i \leqslant j \leqslant n} {\left( { - 1} \right)} } ^{j - i}}{x_i}{x_j}\) and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A n , 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. |
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