A SMASH PRODUCT CONSTRUCTION OF NONLOCAL VERTEX ALGEBRAS
A SMASH PRODUCT CONSTRUCTION OF NONLOCAL VERTEX ALGEBRAS
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DOI：
10.1142/s0219199707002605
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发表时间：
2005-11
影响因子：
1.6
通讯作者：
Haisheng Li
中科院分区：
文献类型：
--
作者：
Haisheng Li
研究了顶点双代数和顶点双代数的非局部顶点模代数的概念，给出了非局部顶点代数的Smash积的构造。对于满足适当条件的非局部顶点代数V，构造了一个标准双代数B（V），使得B（V）的本原元本质上是伪导子，群样元本质上是伪自同态.作为应用，利用Smash积重构了Heisenberg李代数的顶点代数以及非退化偶格的顶点代数，并给出了格顶点代数模的另一种构造方法.
A notion of vertex bialgebra and a notion of nonlocal vertex module-algebra for a vertex bialgebra are studied and then a smash product construction of nonlocal vertex algebras is presented. For every nonlocal vertex algebra V satisfying a suitable condition, a canonical bialgebra B(V) is constructed such that primitive elements of B(V) are essentially pseudo-derivations and group-like elements are essentially pseudo-endomorphisms. As an application, vertex algebras associated with the Heisenberg Lie algebras as well as those associated with the nondegenerate even lattices are reconstructed through smash products, and furthermore, a different approach to the construction of modules for the lattice vertex algebras is given.