We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA $V^G$, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to $V^G$. Applying these methods to extremal lattices in $d=48$ and $d=72$, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states.

我们为非阿贝尔有限自同构群G构造全纯格顶点算子代数的 orbifolds 。为此，我们构建扭曲模块构克用的扶正器的射影表示一起克绞合模块上。这使我们能够提取定点 VOA 的不可约模块${伏}^G$，并计算它们的特征和模变换属性。然后我们通过连接这些模块来构建全纯 VOAs${伏}^G$. 将这些方法应用于极值点阵$d=48$ 和 $d=72$，我们构建了 50 多个新的中心电荷 48 和 72 的全纯 VOA，其中许多具有非常少的光态。