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arXiv · 1710.07917

On nondiagonal finite quasi-qantum groups over finite abelian groups

Hua-Lin Huang·Yuping Yang·Yinhuo Zhang
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Abstract

In this paper, we initiate the study of nondiagonal finite quasi-quantum groups over finite abelian groups. We mainly study the Nichols algebras in the twisted Yetter-Drinfeld module category $_{\k G}^{\k G}\mathcal{YD}^\Phi$ with $\Phi$ a nonabelian $3$-cocycle on a finite abelian group $G.$ A complete clarification is obtained for the Nichols algebra $B(V)$ in case $V$ is a simple twisted Yetter-Drinfeld module of nondiagonal type. This is also applied to provide a complete classification of finite-dimensional coradically graded pointed coquasi-Hopf algebras over abelian groups of odd order and confirm partially the generation conjecture of pointed finite tensor categories due to Etingof, Gelaki, Nikshych and Ostrik.

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Hua-Lin Huang, Yuping Yang, Yinhuo Zhang. 2017-10-22. On nondiagonal finite quasi-qantum groups over finite abelian groups. https://arxiv.org/abs/1710.07917

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