Left-symmetric conformal algebras and vertex algebras☆
Left-symmetric conformal algebras and vertex algebras☆
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DOI：
10.1016/j.jpaa.2014.12.012
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发表时间：
2015-08
影响因子：
0.8
通讯作者：
Yanyong Hong;Fang Li
中科院分区：
文献类型：
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作者：
Yanyong Hong;Fang Li
顶点代数是二维共形场论的代数对应物。利用Bakalov和Kac在[3]中给出的利用李保形代数和左对称代数对顶点代数的等价刻画，在研究顶点代数时，我们必须处理这样一个问题：在一类特殊的李代数形式分布李代数上，是否存在相容的左对称代数结构？本文对此问题进行了研究。介绍了左对称共形代数和Novikov共形代数的定义。得到了这些代数的许多例子。作为应用，我们给出了用左对称共形代数构造顶点代数的方法。
A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. By an equivalent characterization of vertex algebra using Lie conformal algebra and left-symmetric algebra given by Bakalov and Kac in [3], in studying vertex algebra, we have to deal with such a question: Do there exist compatible left-symmetric algebra structures on a class of special Lie algebras named formal distribution Lie algebras? In this paper, we study this question. We introduce the definitions of left-symmetric conformal algebra and Novikov conformal algebra. Many examples of these algebras are obtained. As an application, we present a construction of vertex algebra using left-symmetric conformal algebra.