论文标题
水ech晶格顶点操作员代数的广义深孔的格子理论解释
A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra
论文作者
论文摘要
我们对水ech晶格VOA $v_λ$的广义深孔进行了晶格理论解释。我们表明，一个广义的深孔定义了水ech晶格的“真实”自动形态不变孔。我们还表明，在具有非阿布莱恩$ v_1 $的全体形态voa $ v $的同构类别的同构类别之间存在对应关系。它提供了一种新的组合方法，以分类中央电荷的全态VOA $ 24 $。特别是，我们为观察G.Höhn的观察提供了解释，它将重量的重量与与Niemeier Lattices的胶水代码相关的某些代码字$ 24 $的全态VOA的代数为代数。
We give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA $V_Λ$. We show that a generalized deep hole defines a "true" automorphism invariant deep hole of the Leech lattice. We also show that there is a correspondence between the set of isomorphism classes of holomorphic VOA $V$ of central charge $24$ having non-abelian $V_1$ and the set of equivalence classes of pairs $(τ, \tildeβ)$ satisfying certain conditions, where $τ\in Co_0$ and $\tildeβ$ is a $τ$-invariant deep hole of squared length $2$. It provides a new combinatorial approach towards the classification of holomorphic VOAs of central charge $24$. In particular, we give an explanation for an observation of G. Höhn, which relates the weight one Lie algebras of holomorphic VOAs of central charge $24$ to certain codewords associated with the glue codes of Niemeier lattices.
