Rigidity of maps from Hopf algebras to group algebras

Braided Hopf Algebras Obtained from Coquasitriangular Hopf Algebras

Let (H, σ) be a coquasitriangular Hopf algebra, not necessarily finite dimensional. Following methods of Doi and Takeuchi, which parallel the constructions of Radford in the case of finite dimensional quasitriangular Hopf algebras, we define Hσ , a sub-Hopf algebra of H, the finite dual of H. Using the generalized quantum double construction and the theory of Hopf algebras with a projection, we...

The Grothendieck Group of Hopf Algebras

Let H be a cosemisimple Hopf algebra over an algebraically closed field k. Assume that H contains a simple subcoalgebra of dimension 9. We show that if H has no simple subcoalgebras of even dimension then H contains either a grouplike element with order 2 or 3, a Hopf subalgebra of dimension 75, or a family of simple subcoalgebras whose dimensions are the squares of each positive odd integer. I...

Baxter Algebras and Hopf Algebras

George E. Andrews Department of Mathematics Pennsylvania State University University Park, PA 16802, USA ([email protected]) Li Guo Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]) William Keigher Department of Mathematics and Computer Science Rutgers University at Newark Newark, NJ 07102, USA ([email protected]...

Degeneration, rigidity and irreducible components of Hopf algebras

The aim of this work is to discuss the concepts of degeneration, deformation and rigidity of Hopf algebras and to apply them to the geometric study of the varieties of Hopf algebras. The main result is the description of the ndimensional rigid Hopf algebras and the irreducible components for n = p, p is prime number, and for n < 14. This paper is organized as follows : first we present the basi...

On the Coderivations of Some Hopf Algebras