On cross product Hopf algebras

Cross Product Quantisation, Nonabelian Cohomology and Twisting of Hopf Algebras

This is an introduction to work on the generalisation to quantum groups of Mackey’s approach to quantisation on homogeneous spaces. We recall the bicrossproduct models of the author, which generalise the quantum double. We describe the general extension theory of Hopf algebras and the nonAbelian cohomology spaces H(H,A) which classify them. They form a new kind of topological quantum number in ...

The # Product in Combinatorial Hopf Algebras

We show that the #-product of binary trees introduced by Aval and Viennot [1] is in fact defined at the level of the free associative algebra, and can be extended to most of the classical combinatorial Hopf algebras.

On the Cohomology of a Smash Product of Hopf Algebras

A five term sequence for the low degree cohomology of a smash product of (cocommutative) Hopf algebras is obtained, generalizing that of Tahara for a semi-direct product of groups

On the Coderivations of Some Hopf Algebras

NOTES ON REGULAR MULTIPLIER HOPF ALGEBRAS

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition