Representations of vertex operator algebras over an arbitrary field
Representations of vertex operator algebras over an arbitrary field
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任意域上的顶点算子代数的表示
DOI：
10.1016/j.jalgebra.2014.01.007
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发表时间：
2014-02-01
影响因子：
0.9
通讯作者：
Ren, Li
中科院分区：
文献类型：
--
作者：
Dong, Chongying;Ren, Li
构造了任意代数闭域F上顶点算子代数的结合代数A（V），使得不可约A（V）-模与不可约容许V-模之间存在一一对应.此外，如果V是有理数，则A（V）是半单的。对任意可容许的V-模M构造了一个A（V）-双结节A（M），并研究了它与融合规则的关系.这些结果然后被用来计算与中心电荷为1/2的Virasoro代数的不可约最高权模相关联的有理顶点算子代数L（1/2，0）（F）的融合规则。（C）2014 Elsevier Inc. All rights reserved.
An associative algebra A(V) for a vertex operator algebra over an arbitrary algebraically closed field F is constructed such that there is a one to one correspondence between irreducible A(V)-modules and irreducible admissible V-modules. Moreover, A(V) is semisirnple if V is rational. An A(V)-birnodule A(M) is also constructed for any admissible V-module M and its connection with the fusion rules is investigated. These results are then used to compute the fusion rules for the rational vertex operator algebra L(1/2, 0)(F) associated to the irreducible highest weight module for the Virasoro algebra with central charge 1/2. (C)2014 Elsevier Inc. All rights reserved.