On Nichols algebras over basic Hopf algebras

NICOLÁS ANDRUSKIEWITSCH; IVÁN ANGIONO

MATHEMATISCHE ZEITSCHRIFT

SPRINGER

Lugar: Berlin; Año: 2020 vol. 296 p. 1429 - 1469

0025-5874

This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field k 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.