Hopf Algebras and Tensor Categories

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 normalised class sum and generalised 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.