In this article we develop some aspects of the construction of new Hopf algebras found recently by Andruskiewitsch and Schneider [AS1]. There the authors classified (under some slight restrictions) all pointed finite dimensional Hopf algebras with coradical (Z/p) s . We contribute to this work by giving a closer description of the possible "exotic" linkings. * This work will be part of the author's Ph.D. thesis written under the supervision of Professor H.-J. Schneider. The author is a member of the Graduiertenkolleg "Mathematik im Bereich ihrer Wechselwirkung mit der Physik" at Munich University.

We show that a large class of finite dimensional pointed Hopf algebras is quasi-isomorphic to their associated graded version coming from the coradical filtration, i.e. they are 2-cocycle deformations of the latter. This supports a slightly specialized form of a conjecture in [M]. IntroductionRecently there has been a lot of progress in determining the structure of pointed Hopf algebras. This has led to a discovery of whole new classes of such Hopf algebras and to some important classification results. See the survey article [AS4] for an introduction and references. A lot of these classes contain infinitely many non-isomorphic Hopf algebras of the same dimension, thus disproving an old conjecture of Kaplansky. Masuoka showed in [M], and in a private note, that for certain of these new families the Hopf algebras are all 2-cocycle deformations of each other. This led him to weaken Kaplansky's conjecture, stating that up to quasi-isomorphisms there should only be a finite number of Hopf algebras of a given dimension. This was disproved in [EG] for a family of Hopf algebras of dimension 32. However, our results support Masuoka's conjecture in a really big class of * This work will be part of the author's Ph.D. thesis written under the supervision of Professor H.-J. Schneider. The author is a member of the Graduiertenkolleg "Mathematik im Bereich ihrer Wechselwirkung mit der Physik" at Munich University.

We investigate the question of covariant differential calculi on the bosonisation of a coquasitriangular Hopf algebra and an associated braided Hopf algebra. As a result we present a general way of obtaining such calculi on inhomogeneous quantum groups. *