Nonlocal vertex algebras generated by formal vertex operators
Nonlocal vertex algebras generated by formal vertex operators
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DOI：
10.1007/s00029-006-0017-1
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发表时间：
2005-02
期刊：
影响因子：
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通讯作者：
Haisheng Li
中科院分区：
文献类型：
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作者：
Haisheng Li
这是第一篇研究无穷维量子群（量子仿射代数和杨氏）中顶点代数类对象的系列论文。在本文中，我们奠定了这项研究的基础。对任意向量空间W，我们研究了Hom（W，W（（x）的拟相容子集，证明了任意极大拟相容子空间都具有一个自然非局部（即非交换）顶点代数结构，其中Was是一个自然忠实拟模，并且任意拟相容子集生成一个非局部顶点代数，其中Was是一个拟模.特别地，取W为量子仿射代数的最高权模，得到了Was为拟模的非局部顶点代数。我们还提出并研究了量子顶点代数的概念，给出了非局部顶点代数、量子顶点代数及其模的一般构造。
This is the first paper in a series to study vertex algebra-like objects arising from infinite-dimensional quantum groups (quantum affine algebras and Yangians). In this paper we lay the foundations for this study. For any vector spaceW, we study what we call quasi compatible subsets of Hom (W,W((x))) and we prove that any maximal quasi compatible subspace has a natural nonlocal (namely noncommutative) vertex algebra structure withWas a natural faithful quasi module in a certain sense, and that any quasi compatible subset generates a nonlocal vertex algebra withWas a quasi module. In particular, takingWto be a highest weight module for a quantum affine algebra we obtain a nonlocal vertex algebra withWas a quasi module. We also formulate and study a notion of quantum vertex algebra and we give general constructions of nonlocal vertex algebras, quantum vertex algebras and their modules.