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arXiv · 1605.03995

On Hopf Algebras over quantum subgroups

Gaston Andres Garcia·Joao Matheus Jury Giraldi
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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 ${\mathcal{K}}$ and the corresponding infinitesimal module is an indecomposable object in ${}^{{\mathcal{K}}}_{{\mathcal{K}}}\mathcal{YD}$ (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.

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BibTeXRIS

Gaston Andres Garcia, Joao Matheus Jury Giraldi. 2016-05-12. On Hopf Algebras over quantum subgroups. https://doi.org/10.1016/j.jpaa.2018.04.018

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