New Trends in Hopf Algebra Theory: Proceedings of the Colloquium on Quantum Groups and Hopf Algebras, LA Falda, Sierras De Cordoba, Argentina, August 9-13, 1999

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  • Format: Paperback
  • Copyright: 2001-01-01
  • Publisher: Amer Mathematical Society

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This volume presents the proceedings from the Colloquium on Quantum Groups and Hopf Algebras held in Cordoba (Argentina) in 1999. The meeting brought together researchers who discussed recent developments in Hopf algebras, one of the most important being the influence of quantum groups. 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.

Table of Contents

Infinitesimal Hopf algebras
Modules over weak entwining structures
On generalized characters
BiFrobenius algebras
Integrable models and star structures
On Nichols algebras of low dimension
A generalization of crossed products
A brief introduction to face algebras
On two proofs for the existence and uniqueness of integrals for finite-dimensional Hopf algebras
Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension
Pointed indecomposable Hopf algebras over Coxeter groups
A duality theorem for quantum groupoids
Primitive elements in a free dendriform algebra
On operator representations of $U_q(isl(2,\mathbb{R}))$
Duals and doubles of quantum groupoids ($\times_R$-Hopf algebras)
Survey of braided Hopf algebras
Inner and outer actions of pointed Hopf algebras
Quasi-triangular structures on Hopf algebras with positive bases
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