On the Structure of Framed Vertex Operator Algebras and Their Pointwise Frame Stabilizers
On the Structure of Framed Vertex Operator Algebras and Their Pointwise Frame Stabilizers
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DOI：
10.1007/s00220-007-0323-2
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发表时间：
2006-05
影响因子：
2.4
通讯作者：
C. Lam;H. Yamauchi
中科院分区：
文献类型：
--
作者：
C. Lam;H. Yamauchi
在本文中，我们研究了通用框架顶点算子代数（VOA）的结构。我们证明了框架 VOAV 的结构代码 (C,D) 满足某些对偶条件。因此，我们证明每个帧 VOA 都是相关二进制代码 VOAVC 的简单当前扩展。这个结果表明了对框架顶点算子代数进行分类的可行性，至少在中心电荷很小的情况下。另外，还研究了Vis的点式帧稳定器。我们完全确定了点稳定器中的所有自同构，其阶数为 1、2 或 4。著名的 Moonshine VOA 的 4A 扭曲扇形和 4A 扭曲轨道理论也被明确构造。我们验证了这个扭曲扇区的顶部模块的尺寸为1，重量为3/4，并且通过4A扭曲轨道结构获得的VOA与其自身同构。
In this paper, we study the structure of a general framed vertex operator algebra (VOA). We show that the structure codes (C,D) of a framed VOAVsatisfy certain duality conditions. As a consequence, we prove that every framed VOA is a simple current extension of the associated binary code VOAVC. This result suggests the feasibility of classifying framed vertex operator algebras, at least if the central charge is small. In addition, the pointwise frame stabilizer ofVis studied. We completely determine all automorphisms in the pointwise stabilizer, which are of order 1, 2 or 4. The 4A-twisted sector and the 4A-twisted orbifold theory of the famous moonshine VOAare also constructed explicitly. We verify that the top module of this twisted sector is of dimension 1 and of weight 3/4 and the VOA obtained by 4A-twisted orbifold construction ofis isomorphic toitself.