Hopf Algebras and Quantum Groups

STEFAAN CAENEPEEL is a Professor in the Faculty of Applied Sciences at the Free University of Brussels, Belgium. The coauthor of Brauer Groups and the Cohomology of Graded Rings and coeditor of Rings, Hopf Algebras, and Brauer Groups (both titles, Marcel Dekker, Inc.) and the author or coauthor of over 40 professional papers that reflect his research interests in Brauer groups of graded rings, Hopf algebras, and related subjects, he is the Treasurer of the Belgian Mathematical Society and a member of the American Mathematical Society and the European Mathematical Society, among other organizations. Dr. Caenepeel received the Ph.D. degree (1984) and the habilitation (1991) in mathematics from the Free University of Brussels, Belgium. FREDDY VAN OYSTAEYEN is a Professor of Mathematics at the University of Antwerp/VIA, Belgium. The author, coauthor, editor, or coeditor of over 200 articles, proceedings, book chapters, and books, including Brauer Groups and the Cohomology of Graded Rings, Commutative Algebra and Algebraic Geometry, A Primer of Algebraic Geometry, and Interactions Between Ring Theory and Representations of Algebras (all titles, Marcel Dekker, Inc.), he is a board member of the Belgium Mathematical Society and a member of the Liaisons Committee of the European Mathematical Society. Professor Van Oystaeyen received the Ph.D. degree ( 1972) in mathematics from the Free University of Amsterdam, The Netherlands, and the habilitation (1975) from the University of Antwerp, VIA, Belgium.

• Lifting of Nichols algebras of type A2 and pointed Hopf algebras of order p4; survey of cross product bialgebras; a Morita-Takeuchi context for graded coalgebras; coalgebra-Galois extensions from the extension theory point of view; separable functors for the category of Doi-Hopf modules II; cyclic cohomology of coalgebras, coderivations and De Rham cohomology; Schur-Weyl categories and non-quasiclassical Weyl type formula; a generalized power map for Hopf algebras; associated varieties for classical lie superalgebras; algebraic versions of a finite-dimensional quantum groupoid; quasi-Hopf algebras and the centre of a tensor category; an easy proof for the uniqueness of integrals; the coquasitriangular Hopf algebra associated to a rigid Yang-Baxter coalgebra; on regularity of the algebra of covariants for actions of pointed Hopf algebras on regular commutative algebras; a survey on multiplier Hopf algebras.