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

2024/03/07 by Hua-Lin Huang, Huang, Hua-Lin, Gongxiang Liu +5 · 3 citations
Mathematics · #advanced mathematical theories #Algebraic structures and combinatorial models #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2403.04455

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

Related

• On nondiagonal finite quasi-qantum groups over finite abelian groups
• Finite-dimensional quasi-Hopf algebras of Cartan type
• Finite quasi-quantum groups of rank two
• Module categories over pointed Hopf algebras
• Pointed Hopf algebras over non-abelian groups with non-simple standard braidings