Classification of Balinsky–Novikov superalgebras with dimension 2|2
Classification of Balinsky–Novikov superalgebras with dimension 2|2
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DOI：
10.1088/1751-8113/45/22/225201
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发表时间：
2012-06
期刊：
影响因子：
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通讯作者：
Yan Wang;Zhiqi Chen;C. Bai
中科院分区：
文献类型：
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作者：
Yan Wang;Zhiqi Chen;C. Bai
引入Balinsky-Novikov（BN）超代数的概念，构造了超Virasoro型李超代数.我们将2|奇部积不为零的二维复BN超代数。除了已知的关于分类的结果2|二维Novikov超代数，我们给出了它们与相应的李超代数之间的一个明确的比较.作为应用，我们构造了偶部分为W（2，2）李代数的李超代数.最后，我们重新制定的分类结果的偶数部分是已知的分类结果的二维Novikov代数。
The notion of Balinsky–Novikov (BN) superalgebra was introduced to construct super-Virasoro-type Lie superalgebras. We classify the 2|2-dimensional complex BN superalgebras whose odd parts’ products are not zero. In addition to the known results on the classification of 2|2-dimensional Novikov superalgebras, we give an explicit comparison among them and their associated Lie superalgebras. As an application, we construct some Lie superalgebras whose even parts are the W(2, 2) Lie algebra. Finally, we reformulate the classification results in terms of the even parts being the known classification results of two-dimensional Novikov algebras.