Modular quasi-Hopf algebras and groups with one involution

DOI10.1016/J.JPAA.2022.107264arXiv2203.05500MaRDI QIDQ6393361

Geoffrey Mason, Siu-Hung Ng

Publication date: 10 March 2022

Abstract: In a previous paper the authors constructed a class of quasi-Hopf algebras $D^{omega}(G,A)$ 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 $Rep(D^{omega}(G,A))$ 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 $Rep(D^{omega}(G,A))$ is super-modular rather than modular. We give some explicit examples involving binary polyhedral groups and some sporadic simple groups.

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Cohomology of groups (20J06) Vertex operators; vertex operator algebras and related structures (17B69) Hopf algebras and their applications (16T05) Fusion categories, modular tensor categories, modular functors (18M20)

This page was built for publication: Modular quasi-Hopf algebras and groups with one involution

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6393361)