Pointed Hopf algebras as cocycle deformations

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 results by Masuoka about Morita-Takeuchi equivalence and by Schauenburg about Hopf Galois extensions. We also outline a method to describe the deforming cocycles involved using the exponential map and its q-analogue.

28 pages

References in corpus (2)

• Pointed and copointed Hopf algebras as cocycle deformations
• Cohomological aspects of Hopf algebra liftings

Cited by in corpus (9)

• Deformation by cocycles of pointed Hopf algebras over non-abelian groups
• Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra
• Finite-dimensional Nichols algebras over dual Radford algebras
• On Hopf algebras over basic Hopf algebras of dimension 24
• On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property
• Classification of finite-dimensional Hopf algebras over dual Radford algebras
• Multiparameter quantum groups, bosonizations and cocycle deformations
• Formal multiparameter quantum groups, deformations and specializations
• Cocycle deformations for liftings of quantum linear spaces