Hopf algebras : proceedings from the International Conference at DePaul University, [Chicago, Illinois, February 1-3, 2002

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. 1. Infinitesimal Bialgebras, Pre-lie And Dendriform Algebras / Marcelo Aguiar 1 -- 2. Some Remarks On Nichols Algebras / Nicolas Andruskiewitsch 35 -- 3. The Coradical Of The Dual Of A Lifting Of A Quantum Plane / Nicolas Andruskiewitsch, M. Beattie 47 -- 4. Representations Of Two-parameter Quantum Groups And Schur-weyl Duality / Georgia Benkart, Sarah Witherspoon 65 -- 5. A New Proof Of The Skolem-noether Theorem / Jeffrey Bergen 93 -- 6. Projectivity Of A Relative Hopf Module Over The Subring Of Coinvariants / S. Caenepeel, T. Guedenon 97 -- 7. A Brief Introduction To Coalgebra Representation Theory / William Chin 109 -- 8. Some Examples Of Integrals For Bialgebras / S. Dascalescu 133 -- 9. Bi-frobenius Algebras And Group-like Algebras / Yukio Doi 143 -- 10. Bialgebras And Realizations / R.l. Grossman, R.g. Larson 157 -- 11. Relatively Free Coalgebras / Mikhail Kochetov 167 -- 12. Example Of Almost Commutative Hopf Algebras Which Are Not Coquasitriangular / Akira Masuoka 185 -- 13. Hopf Algebras Of Dimension P[superscript 2] / Siu-hung Ng 193 -- 14. Support Cones For Infinitesimal Group Schemes / Julia Pevtsova 203 -- 15. Coalgebras From Formulas / Serban Raianu 215 -- 16. Fourier Theory For Coalgebras, Bicointegrals And Injectivity For Bicomodules / Walter Ricardo Ferrer Santos 225 -- 17. Notes On The Classification Of Hopf Algebras Of Dimension Pq / Alex Schuler 241 -- 18. A Hopf Algebraic Morita Invariant / Mitsuhiro Takeuchi 253. Edited By Jeffrey Bergen, Stefan Catoiu, William Chin. Includes Bibliographical References. ABSTRACT. We introduce the categories of infinitesimal Hopf modules and bi-modules over an infinitesimal bialgebra.