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

2024/03/07 by Hua-Lin Huang, Huang, Hua-Lin, Gongxiang Liu +5 · 4 citations
Mathematics · #Abelian group #Algebraic structures and combinatorial models #Elementary abelian group #Mathematical and Theoretical Analysis #Mathematics #Physics #Political science #Pure mathematics #Quantum #Quantum mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.04455

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2024/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Reflection of Nichols Algebras over Coquasi-Hopf Algebras
• Pointed Hopf algebras revisited, with a view from tensor categories
• Biproduct Quasi-Hopf Algebras of Rank 2
• On the classification of finite GK-dimensional pre-Nichols algebras and quasi-quantum groups

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• Finite-dimensional quasi-Hopf algebras of Cartan type
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