BALINSKY–NOVIKOV SUPERALGEBRAS AND SOME INFINITE-DIMENSIONAL LIE SUPERALGEBRAS
BALINSKY–NOVIKOV SUPERALGEBRAS AND SOME INFINITE-DIMENSIONAL LIE SUPERALGEBRAS
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DOI：
10.1142/s0219498812501198
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发表时间：
2012-11
影响因子：
0.8
通讯作者：
Yufeng Pei;C. Bai
中科院分区：
文献类型：
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作者：
Yufeng Pei;C. Bai
本文回顾了Balinsky-Novikov（BN）超代数，并讨论了利用BN超代数的仿射化构造无限维李超代数的方法。作为一个例子，我们给出了由两个同构的BN超代数分别构造Beltrami和Green-Schwarz-维滕（GSW）代数的一个显式构造，并作为一个直接推论证明了它们是同构的.此外，我们还考虑了BN超代数通过其相应的BN超代数上的某些双线性形式导出的无限维李超代数的中心扩张。
In this paper, we recall the Balinsky–Novikov (BN) superalgebras and revisit the approach of constructing an infinite-dimensional Lie superalgebra by a kind of affinization of a BN superalgebra. As an example, we give an explicit construction of Beltrami and Green–Schwarz–Witten (GSW) algebras from two isomorphic BN superalgebras, respectively, which proves that they are isomorphic as a direct consequence. Moreover, we consider the central extensions of the infinite-dimensional Lie superalgebras induced from BN superalgebras through certain bilinear forms on their corresponding BN superalgebras.