A new construction of the moonshine vertex operator algebra over the real number field
A new construction of the moonshine vertex operator algebra over the real number field
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DOI：
10.4007/annals.2004.159.535
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发表时间：
1997-01
影响因子：
4.9
通讯作者：
M. Miyamoto
中科院分区：
文献类型：
--
作者：
M. Miyamoto
给出了月光模顶点算子代数V？，最初是在[FLM2]中构建的。我们将其构造为真实的数域R上的框架VOA。我们还提供了将框架VOA的结构转换为另一个框架VOA的方法。作为应用，我们研究了V Eg上的五种框架VOA结构，并构造了包括V？一个小小的VOA我们的建设的优势之一是，我们能够构建V？作为一个框架VOA的正定不变双线性形式，我们可以很容易地证明，Aut（V？）是怪物简单组。通过类似的方法，我们也构造了具有有限个全自同构群的全纯框架VOA的无穷级数。最后，我们计算了Monster单群的3C元的特征标。
We give a new construction of the moonshine module vertex operator algebra V ? , which was originally constructed in [FLM2]. We construct it as a framed VOA over the real number field R. We also offer ways to transform a structure of framed VOA into another framed VOA. As applications, we study the five framed VOA structures on V Eg and construct many framed VOAs including V ? from a small VOA. One of the advantages of our construction is that we are able to construct V ? as a framed VOA with a positive definite invariant bilinear form and we can easily prove that Aut(V ? ) is the Monster simple group. By similar ways, we also construct an infinite series of holomorphic framed VOAs with finite full automorphism groups. At the end of the paper, we calculate the character of a 3C element of the Monster simple group.