Classification of finite-dimensional Hopf algebras over dual Radford algebras

Abstract

We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradicals are isomorphic to dual Radford algebras of dimension $4p$ for a prime $p>5$. In particular, we obtain families of new examples of finite-dimensional Hopf algebras without the dual Chevalley property.

arXiv comment44 pages

References in corpus (7)

• Nichols algebras that are quantum planes
• Pointed and copointed Hopf algebras as cocycle deformations
• Pointed Hopf algebras as cocycle deformations
• On finite-dimensional Hopf algebras
• On $4n$-dimensional neither pointed nor semisimple Hopf algebras and the associated weak Hopf algebras
• Finite-dimensional Nichols algebras over dual Radford algebras
• On Hopf algebras over basic Hopf algebras of dimension 24

Cited by in corpus (2)

• On Hopf algebras over basic Hopf algebras of dimension 24
• On Hopf algebras whose coradical is a cocentral abelian cleft extension