  This is a contribution to the classification of finite-dimensional Hopf
algebras over an algebraically closed field $\Bbbk$ of characteristic 0.
Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical
is basic is a lifting of a Nichols algebra of a semisimple Yetter-Drinfeld
module and we explain how to classify Nichols algebras of this kind. We provide
along the way new examples of Nichols algebras and Hopf algebras with finite
Gelfand-Kirillov dimension.
