1st Edition

Hopf Algebras in Noncommutative Geometry and Physics

Edited By Stefaan Caenepeel, Fred Van Oystaeyen Copyright 2005
    340 Pages 4 B/W Illustrations
    by CRC Press

    340 Pages
    by CRC Press

    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.

    Preface -- Conference Participants -- 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. Bõhm -- 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. Gómez-Torrecillas -- Quantized Coin variants at Transcendental q -- /K. R. Good earl and T. H. Lenagan -- Classification of Differentials on Quantum Doubles and Finite Noncommutative Geometry -- /S. Majid -- Noncommutative Differentials and Yang-Mills on Permutation Groups Sn -- /5. 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. Szlachányi -- On Galois Corings -- /R. Wisbauer.


    Stefaan Caenepeel