论文标题
模块化准-HOPF代数和一组
Modular quasi-Hopf algebras and groups with one involution
论文作者
论文摘要
在上一篇论文中，作者构建了与有限组$ g $相关的一类准Hopf代数$ d^ω（g，a）$，从而推广了扭曲的量子双重结构。我们提供了必要和足够的条件，本质上是同谋，相应的模块类别$ rep（d^ω（g，a））$是一个模块化张量的类别。通用有限群体$ g $的基本理论，也是一个平行理论，涉及$ rep（d^ω（g，a））$ $是超模块化而不是模块化的问题。我们提供了一些涉及二进制多面体组和一些零星简单群体的明确例子。
In a previous paper the authors constructed a class of quasi-Hopf algebras $D^ω(G, A)$ associated to a finite group $G$, generalizing the twisted quantum double construction. We gave necessary and sufficient conditions, cohomological in nature, that the corresponding module category $Rep(D^ω(G, A))$ is a modular tensor category.\ In the present paper we verify the cohomological conditions for the class of groups $G$ which \emph{contain a unique involution}, and in this way we obtain an explicit construction of a new class of modular quasi-Hopf algebras.\ We develop the basic theory for general finite groups $G$, and also a parallel theory concerned with the question of when $Rep(D^ω(G, A))$ is super-modular rather than modular. We give some explicit examples involving binary polyhedral groups and some sporadic simple groups.
