Hopf Algebras and Tensor Categories
About this Title
Nicolás Andruskiewitsch, Universidad Nacional de Córdoba, Córdoba, Argentina, Juan Cuadra, Universidad de Almería, Almería, Spain and Blas Torrecillas, Universidad de Almería, Almería, Spain, Editors
Publication: Contemporary Mathematics
Publication Year 2013: Volume 585
ISBNs: 978-0-8218-7564-3 (print); 978-0-8218-9498-9 (online)
This volume contains the proceedings of the Conference on Hopf Algebras and Tensor Categories, held July 4–8, 2011, at the University of Almería, Almería, Spain.
The articles in this volume cover a wide variety of topics related to the theory of Hopf algebras and its connections to other areas of mathematics. In particular, this volume contains a survey covering aspects of the classification of fusion categories using Morita equivalence methods, a long, self-contained, and comprehensive introduction to Hopf algebras in the category of species, and a summary of the status to date of the classification of Hopf algebras of dimensions up to 100. Among other articles in this volume are a study of normalized class sum and generalized character table for semisimple Hopf algebras, a contribution to the classification program of finite dimensional pointed Hopf algebras, an analysis of conjugacy classes related to a conjecture of De Concini, Kac, and Procesi on representations of quantum groups at roots of unity, a categorical approach to the Drinfeld double of a braided Hopf algebra via Hopf monads, an overview of Hom-Hopf algebras, and several discussions on the crossed product construction in different settings.
Graduate students and research mathematicians interested in Hopf algebra theory, tensor categories, quantum groups, representation theory, and combinatorics and conformal field theory.
Table of Contents
- A. L. Agore and G. Militaru – Unified products and split extensions of Hopf algebras
- Marcelo Aguiar and Swapneel Mahajan – Hopf monoids in the category of species
- Margaret Beattie and Gastón Andrés García – Classifying Hopf algebras of a given dimension
- Gabriella Böhm and José Gómez-Torrecillas – On the double crossed product of weak Hopf algebras
- Alain Bruguières and Alexis Virelizier – The doubles of a braided Hopf algebra
- Giovanna Carnovale – Induced Conjugacy Classes and Induced -Modules
- Miriam Cohen and Sara Westreich – Recovering information from character tables of Hopf algebras: normality, dimensions and quotients
- Mohamed Elhamdadi and Abdenacer Makhlouf – Hom-quasi-bialgebras
- F. Fantino and L. Vendramin – On twisted conjugacy classes of type D in sporadic simple groups
- J. M. Fdez Vilaboa, R. González Rodríguez and A. B. Rodríguez Raposo – Partial and unified crossed products are weak crossed products
- Libin Li and Yinhuo Zhang – The Green rings of the generalized Taft Hopf algebras
- Dmitri Nikshych – Morita equivalence methods in classification of fusion categories