Selecta Mathematica

, Volume 24, Issue 5, pp 4197–4221 | Cite as

On nondiagonal finite quasi-quantum groups over finite abelian groups

  • Hua-Lin Huang
  • Yuping YangEmail author
  • Yinhuo Zhang


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 \(_{\mathbb {k}G}^{\mathbb {k}G}{\mathcal {Y}}{\mathcal {D}}^\Phi \) 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.


Quasi-quantum group Nichols algebra Tensor category 

Mathematics Subject Classification

16T05 18D10 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fujian Province University Key Laboratory of Computational Science, School of Mathematical SciencesHuaqiao UniversityQuanzhouChina
  2. 2.School of Mathematics and StatisticsSouthwest UniversityChongqingChina
  3. 3.Department of Mathematics and StatisticsUniversity of HasseltDiepenbeekBelgium

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