On nondiagonal finite quasi-qantum groups over finite abelian groups

2017/10/22 by Hua-Lin Huang, Yuping Yang, Huang, Hua-Lin +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1710.07917

openalex publication_date 2017/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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}YD^Φ with Φ 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.

Cited by

• Reflection of Nichols Algebras over Coquasi-Hopf Algebras

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