Finite-dimensional Hopf Algebras over the Smallest Non-pointed Basic Hopf Algebra.

Let K be the smallest dimensional non-pointed basic Hopf algebra. We determine all finite-dimensional Nichols algebras in and compute the liftings. The result shows that there are some new Nichols algebras of non-diagonal type and new finite-dimensional Hopf algebras without the dual Chevalley property. [ABSTRACT FROM AUTHOR]