On finite-dimensional copointed Hopf algebras over dihedral groups

Finite Dimensional Pointed Hopf Algebras over S

Formal groups over Hopf algebras

The aim of this section is to define some generalization of the notion of formal group. More precisely, we consider the analog of formal groups with coefficients belonging to a Hopf algebra. We also study some example of a formal group over a Hopf algebra, which generalizes the formal group of geometric cobordisms. Recently some important connections between the Landweber-Novikov algebra and th...

Representations of Finite Dimensional Pointed Hopf Algebras over S 3

The classification of finite-dimensional pointed Hopf algebras with group S3 was finished in [AHS]: there are exactly two of them, the bosonization of a Nichols algebra of dimension 12 and a non-trivial lifting. Here we determine all simple modules over any of these Hopf algebras. We also find the Gabriel quivers, the projective covers of the simple modules, and prove that they are not of finit...

Logarithms of formal groups over Hopf algebras

This paper is the continuation of section 2 of the paper ”Floating bundles and their applications” [1]. Let (H, μ, η,∆, ε, S) be a commutative Hopf algebra over ring R without torsion and F(x ⊗ 1, 1⊗ x) be a formal group over Hopf algebra H. By HQ denote the Hopf algebra H⊗ Z Q over ring RQ = R⊗ Z Q. We shall write μ, η, . . . instead of μQ, ηQ, . . . . The aim of this paper is to prove the fol...

Pointed Hopf Algebras over Non-abelian Groups

The class of finite-dimensional pointed Hopf algebras is a field of current active research. The classification of these algebras has seen substantial progress since the development of the so-called “Lifting method” by Andruskiewitsch and Schneider. With this tool, the case in which the group of group-like elements is abelian is almost completed and recent results by these and other authors suc...