Modular quasi-Hopf algebras and groups with one involution

Authors

Geoffrey Mason, University of California, Santa Cruz
Siu Hung Ng, Louisiana State University

Document Type

Article

Publication Date

5-1-2023

Abstract

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 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.

Publication Source (Journal or Book title)

Journal of Pure and Applied Algebra

Recommended Citation

Mason, G., & Ng, S. (2023). Modular quasi-Hopf algebras and groups with one involution. Journal of Pure and Applied Algebra, 227 (5) https://doi.org/10.1016/j.jpaa.2022.107264