Abstract In 1986, Van de Leur introduced and classified affine Lie superalgebras. An affine Lie superalgebra is defined as the quotient of certain Lie superalgebra G defined by generators and relations, corresponding to a symmetrizable generalized Cartan matrix, over the so-called radical of G . Because of the interesting applications of affine Lie (super)algebras in combinatorics, number theory and physics, it is very important to recognize how far a Lie (super)algebra is to be an affine Lie (super)algebra. In this regard, we determine affine Lie superalgebras axiomatically.

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仿射李超代数

摘要 1986 年，Van de Leur 引入并分类了仿射李超代数。仿射李超代数定义为由生成元和关系定义的特定李超代数 G 的商，对应于可对称广义 Cartan 矩阵，在 G 的所谓根上。由于仿射李（超）代数在组合数学、数论和物理学中的有趣应用，认识到李（超）代数在多大程度上成为仿射李（超）代数非常重要。在这方面，我们公理地确定仿射李超代数。