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

Abstract

We classify finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradcial is isomorphic to the smallest non-pointed basic Hopf algebra, under the assumption that the diagrams are strictly graded. In particular, we obtain some new Nichols algebras of non-diagonal type and new finite-dimensional Hopf algebras without the dual Chevalley property.

This version: 18 pages. This work is a continuation of arXiv:1605.03995

References in corpus (7)

• Nichols algebras that are quantum planes
• Pointed and copointed Hopf algebras as cocycle deformations
• On Hopf Algebras over quantum subgroups
• Pointed Hopf algebras as cocycle deformations
• Some Hopf algebras of dimension $72$ without the Chevalley property
• Eight classes of new Hopf algebras of dimension $128$ without the Chevalley property
• On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property

Cited by in corpus (3)

• On $4n$-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras
• On Hopf algebras over basic Hopf algebras of dimension 24
• On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property