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 Séminaires et Congrès 1997; 294 pp; softcover Number: 2 ISBN-10: 2-85629-052-3 ISBN-13: 978-2-85629-052-1 List Price: US$66 Member Price: US$52.80 Order Code: SECO/2 The seventh meeting of the Contact Franco-Belge was held in Reims in June 1995. The goal of the meeting was the presentation of recent advances in several related areas where a non-commutative algebraic approach is necessary. The first part of the book contains five articles on new progress in classical problems; the second part, five papers on Hopf algebras, quantum groups and their representations; and the third part, six papers on invariant theory and representation theory. Two chapters are in French, remaining chapters are in English. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians. Table of Contents S. S. Abhyankar -- Hilbert's Thirteenth Problem B. Keller -- Basculement et homologie cyclique A. A. Kirillov and A. Melnikov -- On a remarkable sequence of polynomials M. Van den Bergh -- Division algebras on $$\mathbb P^2$$ of odd index, ramified along a smooth elliptic curve are cyclic A. van den Essen -- Polynomial automorphisms and the Jacobian conjecture S. Caenepeel -- Harrison cocycles and the group of Galois coobjects J. Donin, D. Gurevich, and V. Rubtsov -- Quantum hyberboloid and braided modules S. M. Khoroshkin -- Central extension of the Yangian double C. M. Ringel -- Quantum Serre relations L. Willaert -- Schematic algebras and the Auslander-Gorenstein property M. Brion -- Sur certains modules gradués associés aux produits symétriques A. Joseph -- Coxeter structure and finite group action H. Derksen and H. Kraft -- Constructive invariant theory L. Le Bruyn -- Orbits of matrix tuples O. Mathieu -- Some conjectures about invariant theory and their applications A. Melnikov -- Dense orbits in orbital varieties in $$\mathfrak s\mathfrak l_{n}$$