On the Classification of Finite Quasi-Quantum Groups over Abelian Groups

Gongxiang Liu; Hua-Lin Huang; Yuping Yang; Yu Ye

On the Classification of Finite Quasi-Quantum Groups over Abelian Groups

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arxiv 2403.04455 v1 pith:QLZR7QFY submitted 2024-03-07 math.QA math.RA

Hua-Lin Huang , Gongxiang Liu , Yuping Yang , Yu Ye This is my paper · ORCID

classification math.QAmath.RA

keywords groupsabelianalgebrasfinitefinite-dimensionalpointedcategoriesclassification

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Using a variety of methods developed in the theory of finite-dimensional quasi-Hopf algebras, we classify all finite-dimensional coradically graded pointed coquasi-Hopf algebras over abelian groups. As a consequence, we partially confirm the generation conjecture of pointed finite tensor categories due to Etingof, Gelaki, Nikshych and Ostrik.

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Biproduct Quasi-Hopf Algebras of Rank 2
math.QA 2025-08 conditional novelty 6.0 of 10

Every 2-dimensional braided Hopf algebra over a quasi-Hopf algebra H is either the trivial k[C2] or a member of the explicitly parametrized family B_{σ,v}.

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