Rings, Hopf Algebras, and Brauer Groups

STEFAAN CAENEPEEL is a Professor in the Faculty of Applied Sciences at the Free University of Brussels (VUB), Belgium, and a Professor of Mathematics at Vesalius College, Brussels, Belgium. The coauthor of Brauer Groups and the Cohomology of Graded Rings (Marcel Dekker, Inc.) and the author or coauthor of over 40 professional papers that reflect his research interests in Brauer groups of graded rings, relative Brauer groups, and related subjects, he is 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 mathe¬matics from the Free University of Brussels (VUB), Belgium. ALAIN VERSCHOREN is a Professor in the Department of Mathematics and Computer Science at the University of Antwerp, Belgium. He is the author, coau¬thor, or coeditor of more than 20 books, including Compatibility, Stability, and Sheaves; Relative Invariants of Rings: The Commutative Theory; Relative Invariants of Rings: The Noncommutative Theory; and Relative Invariants of Sheaves (all titles, Marcel Dekker, Inc.) and the author or coauthor of over 120 pro¬fessional papers. Dr. Verschoren is a Laureate of the Belgian Academy of Sciences and a member of the Belgian Mathematical Society, the American Mathematical Society, and the European Mathematical Society. He received the Ph.D. degree (1979) in algebraic geometry and the habilitation (1982) in mathematics from the University of Antwerp, Belgium.

• Sur les invariants des algebres de Weyl et de leurs corps de fractions; a Picard-Brauer five term exact sequence for braided categories; topological methods in algebra; an introduction to effective calculus in quantum groups; Kummer theory for monogenic Larson orders; smash (co)products from adjunctions; module-theoretical properties of good curve singularities; Morita-Takeuchi equivalance, cohomology of coalgebras and Azumaya coalgebras; decomposition of locally finite modules; existence of covers over fixed rings; on the application of the factorization ideals associated to a finite free resolution; division theorem over the Dwork-Monsky-Washnitzer completion of polynomial rings and Weyl algebras; maximal subfields in the quotient division ring of an enveloping algebra; a Maschke-type theorem for quasi-Hopf algebras; when are all the finitely generated modules embeddable in free modules?; skew-primitive elements of quantum groups and braided Lie algebras; involutive invariants of a Krull domain and Amitsur cohomology; the spectrum of Abelian categories and reconstruction of schemes; face algebras are xR-bialgebras; intersection dimension and canonical modules; Brauer groups of actions; an alternative approach to involutive Brauer groups; a new dimension for schematic algebras.