Finite-dimensional Pointed or Copointed Hopf algebras over affine racks

GARCÍA IGLESIAS, AGUSTÍN; VAY, CRISTIAN

JOURNAL OF ALGEBRA

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2014 vol. 397 p. 379 - 406

0021-8693

We study the copointed, respectively pointed, liftings of Nichols algebras associated toaffine racks and constant cocycle over k^G, respectively kG, for any finite groupG admitting a principal YD-realization of the rack. In the copointed case we completethe classification for the four affine racks whose Nichols algebra is known to be offinite dimension. In the pointed case our method allows us to finishthree of them. In all of the cases the Hopf algebras obtained turn out to be cocycledeformations of their associated graded Hopf algebras. All of them are new examples offinite-dimensional copointed or pointed Hopf algebras over non-abelian groups.