Abstract
Let be an algebraically closed field of characteristic zero. We determine all finite-dimensional Hopf algebras over
whose Hopf coradical is isomorphic to the unique 12-dimensional Hopf algebra
without the dual Chevalley property, such that the diagrams are strictly graded and the corresponding infinitesimal braidings are indecomposable objects in
. In particular, we obtain new Nichols algebras of dimension 18 and 36 and two families of new Hopf algebras of dimension 216.
2010 Mathematics Subject Classification:
Acknowledgements
The author is indebted to his supervisors Profs. Giovanna Carnovale and Naihong Hu so much for the kind help and continued encouragement. The author is grateful to Prof. G.-A. Garcia for helpful conversations and comments and also thanks Profs. G.-A. Garcia and L. Vendramin for providing the computation with GAP of Nichols algebras. The author would like to thank the referee for careful reading and helpful suggestions that largely improved the exposition.