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

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

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

Quantum Algebra 2024-03-08 v1 Rings and Algebras

Authors: Hua-Lin Huang , Gongxiang Liu , Yuping Yang , Yu Ye

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.

Keywords

quasi-quantum groups abelian groups quasi-hopf algebras classification pointed finite tensor categories generation conjecture coradically graded

Cite

@article{arxiv.2403.04455,
  title  = {On the Classification of Finite Quasi-Quantum Groups over Abelian Groups},
  author = {Hua-Lin Huang and Gongxiang Liu and Yuping Yang and Yu Ye},
  journal= {arXiv preprint arXiv:2403.04455},
  year   = {2024}
}

Comments

30 pages. arXiv admin note: text overlap with arXiv:1710.07917

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

Abstract

Keywords

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