Constructing quantum vertex algebras
Constructing quantum vertex algebras
复制标题
DOI：
10.1142/s0129167x06003588
复制
发表时间：
2005-05
影响因子：
0.6
通讯作者：
Haisheng Li
中科院分区：
文献类型：
--
作者：
Haisheng Li
这是一个[23]的续集。本文重点研究上量子顶点代数的构造，其概念在[23]中以Etingof和Kazhdan的量子顶点算子代数（[[h]]上）的概念作为主要动机之一。作为构造量子顶点代数的主要步骤之一，我们证明了环n上的每个可数维非局部（即非交换）顶点代数，无论是不可约的还是具有PBW型基的，都是Etingof和Kazhdan意义下的非退化顶点代数.利用这个结果，我们建立了一些著名的顶点算子代数和一些新构造的非局部顶点代数的非退化性。我们构造了一类与Zamolodchikov-Faddeev代数密切相关的量子顶点代数。
This is a sequel to [23]. In this paper, we focus on the construction of quantum vertex algebras over ℂ, whose notion was formulated in [23] with Etingof and Kazhdan's notion of quantum vertex operator algebra (over ℂ[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely, noncommutative) vertex algebra over ℂ, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some newly constructed nonlocal vertex algebras. We construct a family of quantum vertex algebras closely related to Zamolodchikov–Faddeev algebras.