This volume publishes key proceedings from the recent International Conference on Hopf Algebras held at DePaul University, Chicago, Illinois. With contributions from leading researchers in the field, this collection deals with current topics ranging from categories of infinitesimal Hopf modules and bimodules to the construction of a Hopf algebraic Morita invariant. It uses the newly introduced theory of bi-Frobenius algebras to investigate a notion of group-like algebras and summarizes results on the classification of Hopf algebras of dimension pq. It also explores pre-Lie, dendriform, and Nichols algebras and discusses support cones for infinitesimal group schemes.
I. Infinitesimal Bialgebras, Pre-Lie and Dendriform Algebras. 2. Some Remarks on Nichols Algebras. Nicolas Andruskiewitsch. 3. The Coradical of the Dual of a Lifting of a Quantum Plane Nicolas Andruskiewitsch and M Beattie. 4. Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality. 5. A New Proof of the Skolem-Noether Theorem. 6. Projectivity of a Relative Hopf Module over the Subring of Coinvariants. 7. A Brief Introduction to Coalgebra Representation Theory. 8. Some Examples of Integrals for Bialgebras. 9. Bi-Frobenius Algebras and Group-Like Algebras. 10. Bialgebras and Realizations. 11. Relatively Free Coalgebras. 12. Example of Almost Commutative Hopf Algebras Which Are Not Coquasitriangular. 13. Hopf Algebras of Dimension p2. 14. Support Cones for Infinitesimal Group Schemes. 15. Coalgebras from Formulas. 16. Fourier Theory for Coalgebras, Bicointegrals and Injectivity for Bicomodules. 17. Notes on the Classification of Hopf Algebras of Dimension pq. 18. A Hopf Algebraic Morita Invariant