English

On Hopf Algebras over quantum subgroups

Quantum Algebra 2021-12-24 v3

Abstract

Using the standard filtration associated with a generalized lifting method, we determine all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose coradical generates a Hopf subalgebra isomorphic to the smallest non-pointed non-cosemisimple Hopf algebra K{\mathcal{K}} and the corresponding infinitesimal module is an indecomposable object in KKYD{}^{{\mathcal{K}}}_{{\mathcal{K}}}\mathcal{YD} (we assume that the diagrams are Nichols algebras). As a byproduct, we obtain new Nichols algebras of dimension 8 and new Hopf algebras of dimension 64.

Keywords

Cite

@article{arxiv.1605.03995,
  title  = {On Hopf Algebras over quantum subgroups},
  author = {Gaston Andres Garcia and Joao Matheus Jury Giraldi},
  journal= {arXiv preprint arXiv:1605.03995},
  year   = {2021}
}

Comments

First version: 34 pages, with an Appendix. Second version: 26 pages with minor changes in exposure; we also remove Theorem 5.1. Third version: 26 pages; accepted version to appear in J. Pure Appl. Algebra

R2 v1 2026-06-22T13:59:46.427Z