Z3-orbifold construction of the Moonshine vertex operator algebra and some maximal 3-local subgroups of the Monster
Z3-orbifold construction of the Moonshine vertex operator algebra and some maximal 3-local subgroups of the Monster
复制标题
Moonshine 顶点算子代数的 Z3 轨道构造和 Monster 的一些最大 3 局部子群
DOI：
10.1007/s00209-017-1878-z
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发表时间：
2017
影响因子：
0.8
通讯作者：
H. Shimakura
中科院分区：
文献类型：
--
作者：
H.Y. Chen;C.H. Lam;H. Shimakura
本文利用顶点算子代数刻画了Monster单群的一些极大3-局部子群。首先，我们研究了通过对Leech格的顶点算子代数应用orbilold构造而得到的全纯顶点算子代数，以及Leech格的一个3阶不动点自由等距的提升。我们还考虑了它的一些特殊的子VOA，并利用这些子VOA的对称性研究了它们的稳定子群。证明了这些稳定子群是其全自同构群的3-局部子群。作为我们的主要结果之一，我们利用3-局部刻画证明了它的全自同构群与Monster单群同构，全纯VOA与Moonlight VOA同构。通过这种方法，我们可以得到形状的两个极大3-局部子群和Monster单群的相对显式的刻画。
In this article, we describe some maximal 3-local subgroups of the Monster simple group using vertex operator algebras (VOA). We first study the holomorphic vertex operator algebra obtained by applying the orbifold construction to the Leech lattice vertex operator algebra and a lift of a fixed-point free isometry of order 3 of the Leech lattice. We also consider some of its special subVOAs and study their stabilizer subgroups using the symmetries of the subVOAs. It turns out that these stabilizer subgroups are 3-local subgroups of its full automorphism group. As one of our main results, we show that its full automorphism group is isomorphic to the Monster simple group by using a 3-local characterization and that the holomorphic VOA is isomorphic to the Moonshine VOA. This approach allows us to obtain relatively explicit descriptions of two maximal 3-local subgroups of the shapeandin the Monster simple group.