## Pointed and copointed Hopf algebras as cocycle deformations,” arxiv:0709.0120

Citations: | 8 - 2 self |

### BibTeX

@MISC{Grunenfelder_pointedand,

author = {L. Grunenfelder and M. Mastnak},

title = {Pointed and copointed Hopf algebras as cocycle deformations,” arxiv:0709.0120},

year = {}

}

### OpenURL

### Abstract

Abstract. We show that all finite dimensional pointed Hopf algebras with the same diagram in the classification scheme of Andruskiewitsch and Schneider are cocycle deformations of each other. This is done by giving first a suitable characterization of such Hopf algebras, which allows for the application of a result of Masuoka about Morita-Takeuchi equivalence and of Schauenburg about Hopf Galois extensions. The “infinitesimal ” part of the deforming cocycle and of the deformation determine the deformed multiplication and can be described explicitly in terms of Hochschild cohomology. Applications to, and results for copointed Hopf algebras are also considered. Finite dimensional pointed Hopf algebras over an algebraically closed field of characteristic zero, particularly when the group of points is abelian, have been studied quite extensively with various methods in [AS, BDG, Gr1, Mu]. The most far reaching results as yet in this area have been obtained in [AS], where a large