论文标题
顶点操作员代数的扭曲模块和副人分类形态学
Twisted Modules of a Vertex Operator Algebra and Associators as Classifying Morphisms
论文作者
论文摘要
顶点操作员代数$ v $的扭曲模块的单型类别被定义并简化为其2组可逆对象$g_α$，它可以用3个cocycle $α$在其0 truncation $ g $上的3个cocycle $α$描述，其价值与$ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ v $ a的价值。该合子还提出了$ \ infty $ - 组扩展为$ g $ $ g $的分类形态。由此激励，证明由$ \ infty $ group扩展由3循环$α$分类为skeletal 2 group $g_α$与Associator $α$提出。根据月光和$（\ infty，1）$ topos理论的当前发展，讨论了结果。
The monoidal category of twisted modules of a Vertex Operator Algebra $V$ is defined and reduced to its 2-group of invertible objects $G_α$, which can be described by a 3-cocycle $α$ on its 0-truncation $G$ with values in the group of units $A$ of the field of definition of $V$ serving as its associator. This cocycle also presents the classifying morphism of an $\infty$-group extension of $G$ by the delooping $BA$. Motivated by this, it is proven that the $\infty$-group extension classified by a 3-cocycle $α$ is presented by the skeletal 2-group $G_α$ with associator $α$. The results are discussed in light of current developments in Moonshine and $(\infty,1)$-topos theory.
