English

Finite GK-dimensional Nichols algebras over the quaternion group $Q_8$

Quantum Algebra 2023-12-19 v1 Representation Theory

Abstract

We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GK-dimension for short, through the study of Nichols algebras over Q 8 ,the quaternion group . We find all the irreducible Yetter-Drinfeld modules V over Q 8 , and determine which Nichols algebras B(V ) of V are finite GK-dimensional, and which Nichols algebras B(V ) of V are finite dimensional.

Keywords

Cite

@article{arxiv.2312.10505,
  title  = {Finite GK-dimensional Nichols algebras over the quaternion group $Q_8$},
  author = {Yongliang Zhang},
  journal= {arXiv preprint arXiv:2312.10505},
  year   = {2023}
}