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