Hopf algebras in noncommutative geometry and physics : [proceedings of meeting "Hopf algebras and quantum groups", which was held from May 28 until June 1, 2002, at the Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten, the Royal Acad

This comprehensive reference summarizes the proceedings and keynote presentations from a recent conference held in Brussels, Belgium. Offering 1155 display equations, this volume contains original research and survey papers as well as contributions from world-renowned algebraists. It focuses on new results in classical Hopf algebras as well as the classification theory of finite dimensional Hopf algebras, categorical aspects of Hopf algebras, and recent advances in the theory of corings and quasi-Hopf algebras. It provides examples and basic properties of corings and their comodules in relation to ring and Hopf algebra theory and analyzes entwining structures and Morita theory for corings. Content: Morita contexts for corings and equivalences / J. Abuhlail -- Hopf order module algebra orders / F. Aly and F. Van Oystaeyen -- An alternative notion of Hopf algebroid / G. Bohm -- Topological Hopf algebras, quantum groups and deformation quantization / Ph. Bonneau and D. Sternheimer -- On coseparable and biseparable corings / T. Brzezinski, L. Kadison and R. Wisbauer -- More properties of Yetter-Drinfeld modules over quasi-Hopf algebras / D. Bulacu, S. Caenepeel and F. Panaite -- Rationality properties for Morita contexts associated to corings / S. Caenepeel, J. Vercruysse and S.H. Wang -- Morita duality for corings over quasi-Frobenius rings / L. El Kaoutit and J. Gomez-Torrecillas -- Quantized coinvariants at transcendental q / K.R. Goodearl and T.H. Lenagan -- Classification of differentials on quantum doubles and finite noncommutative geometry / S. Majid -- Noncommutative differentials and Yang-Mills on permutation groups S[subscript n] / S. Majid -- The affineness criterion for Doi-Koppinen modules / C. Menini and G. Militaru -- Algebra properties invariant under twisting / S. Montgomery -- Quantum SL(3, C)'s : the missing case / C. Ohn -- Cuntz algebras and dynamical quantum group SU(2) / A. Paolucci -- On symbolic computations in braided monoidal categories / B. Pareigis -- Quotients of finite quasi-Hopf algebras / P. Schauenburg -- Adjointable monoidal functors and quantum groupoids / K. Szlachanyi -- On Galois corings / R. Wisbauer. This volume contains the proceedings of meeing "Hopf algebras and quantum groups", which was held frommay 28 until June 1, 2002, at the Koninklijke Vlaamse Academie van Belgie voor Wetenschappen en Kunsten, the Royal Academy loacted in ... Brussels. The conference focused at new results on classical Hopf algebras, categorical aspects of Hopf algebras, connections with Mathematical physics and the recent devvelopments in the theory of corings and of quasi-Hopf algebra.[From Preface] Summarizes the proceedings and keynote presentations from a conference held in Brussels, Belgium. This work focuses on results in classical Hopf algebras as well as the classification theory of finite dimensional Hopf algebras, categorical aspects of Hopf algebras, and advances in the theory of corings and quasi-Hopf algebras. ABSTRACT. In this note we study Morita contexts and Galois extensions for corings.