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## Generators and relations for (generalised) Cartan type superalgebras. (arXiv:1812.03068v1 [math.RT])

In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, \$A(n-1,0) = \mathfrak{sl}(1|n)\$ can be constructed by adding a "gray" node to the Dynkin diagram of \$A_{n-1} = \mathfrak{sl}(n)\$, corresponding to an odd null root. The Cartan superalgebras constitute a different class, where the simplest example is \$W(n)\$, the derivation algebra of the Grassmann algebra on \$n\$ generators. Here we present a novel construction of \$W(n)\$, from the same Dynkin diagram as \$A(n-1,0)\$, but with additional generators and relations.查看全文

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 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For example, \$A(n-1,0) = \mathfrak{sl}(1|n)\$ can be constructed by adding a "gray" node to the Dynkin diagram of \$A_{n-1} = \mathfrak{sl}(n)\$, corresponding to an odd null root. The Cartan superalgebras constitute a different class, where the simplest example is \$W(n)\$, the derivation algebra of the Grassmann algebra on \$n\$ generators. Here we present a novel construction of \$W(n)\$, from the same Dynkin diagram as \$A(n-1,0)\$, but with additional generators and relations.
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