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 and the corresponding infinitesimal module is an indecomposable object in (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.
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