Lifting via cocycle deformation Page 1 Journal of Pure and Applied Algebra 218 (2014) 684–703
Contents lists available at ScienceDirect Journal of Pure and Applied Algebra journal …

After the classification of the finite-dimensional Nichols algebras of diagonal type 17, 18, the
determination of its defining relations 7, 6, and the verification of the generation in degree-s1 …

Let H be a Hopf algebra over a field K of characteristic 0 and let A be a bialgebra or Hopf
algebra such that H is isomorphic to a sub-Hopf algebra of A and there is an H-bilinear …

We introduce a method to construct explicitly multiplicative 2-cocycles for bosonizations of
Nichols algebras B (V) over Hopf algebras H. These cocycles arise as liftings of H-invariant …

Over a field of prime characteristic p> 2, we prove that the cohomology rings of some pointed
Hopf algebras of dimension p 3 are finitely generated. These are Hopf algebras arising in …

We classify finite-dimensional pointed Hopf algebras with abelian coradical, up to
isomorphism, and show that they are cocycle deformations of the associated graded Hopf …

In this paper we study the properties of Drinfeld's twisting for finite-dimensional Hopf
algebras. We determine how the integral of the dual to a unimodular Hopf algebra H …

We show that semisimple Hopf algebras having a self-dual faithful irreducible comodule of
dimension 2 are always obtained as abelian extensions with quotient Z2. We prove that …

In this survey, we first review some known results on the representation theory of algebras
with triangular decomposition, including the classification of the simple modules. We then …

Using the standard filtration associated with a generalized lifting method, we determine all
finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero …