New Trends in Hopf Algebra Theory

Articles offer introductory expositions and surveys on topics of current interest that, to date, have not been available in the current literature. Surveys are included on characteristics of Hopf algebras and their generalizations, biFrobenius algebras, braided Hopf algebras, inner actions and Galois theory, face algebras, and infinitesimal Hopf algebras. The following topics are also covered: existence of integrals, classification of semisimple and pointed Hopf algebras, $*$-Hopf algebras, dendriform algebras, etc. Non-classical topics are also included, reflecting its applications both inside and outside the theory.

Contents

• M. Aguiar -- Infinitesimal Hopf algebras
• S. Caenepeel and E. De Groot -- Modules over weak entwining structures
• M. Cohen -- On generalized characters
• Y. Doi and M. Takeuchi -- BiFrobenius algebras
• A. García and R. Trinchero -- Integrable models and star structures
• M. Graña -- On Nichols algebras of low dimension
• J. A. Guccione and J. J. Guccione -- A generalization of crossed products
• T. Hayashi -- A brief introduction to face algebras
• L. H. Kauffman and D. E. Radford -- On two proofs for the existence and uniqueness of integrals for finite-dimensional Hopf algebras
• A. Masuoka -- Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension
• A. Milinski and H.-J. Schneider -- Pointed indecomposable Hopf algebras over Coxeter groups
• D. Nikshych -- A duality theorem for quantum groupoids
• M. Ronco -- Primitive elements in a free dendriform algebra
• S. Sachse -- On operator representations of $U_q(isl(2,\mathbb{R}))$
• P. Schauenburg -- Duals and doubles of quantum groupoids ($\times_R$-Hopf algebras)
• M. Takeuchi -- Survey of braided Hopf algebras
• S. Westreich -- Inner and outer actions of pointed Hopf algebras
• J.-H. Lu, M. Yan, and Y. Zhu -- Quasi-triangular structures on Hopf algebras with positive bases