On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property

Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra

“…This work is a continuation of the paper [GG16] on the classification of finite-dimensional Hopf algebras over k without the dual Chevalley property, that is, the coradical is not a subalgebra. Until now, there are few concrete examples of such Hopf algebras without pointed duals, with some exceptions in [GG16,HX17,X17]. Let K be the smallest Hopf algebra without the dual Chevalley property.…”

On $4n$-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras

“…Based on this, [32] determined all finite-dimensional Nichols algebras over the semisimple objects in H8 H8 Y D and obtained some new Nichols algebras of non-diagonal type and new Hopf algebras without the dual Chevalley property. By the equivalence M D(H 12 ) ≃ H12 H12 Y D, the authors ( [11], [33]) obtained some new Nichols algebras which were not of diagonal type and some families of new Hopf algebras of dimension 216.…”