Pointed and copointed Hopf algebras as cocycle deformations

Details Pointed and copointed Hopf algebras as cocycle deformations Pointed and copointed Hopf algebras as cocycle deformations

2007-09-02

arxiv.org/abs/0709.0120v2

Mathematics

Rings and Algebras

44 pages

Scientific paper

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.

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