Preface
The international conference Hopf Algebras and Tensor Categories was held at
the University of Almer´ ıa (Spain) from July 4 to July 8, 2011. It was attended by
80 researchers coming from 23 different countries. Around a quarter of them were
young researchers. There were 24 invited talks and 28 contributed talks. The list
of participants and conference program is included later. In the web page of the
meeting http://www.ual.es/Congresos/hopf2010/ one can find the abstract of
all talks and the slides presentation of many of them. The organizing committee
consisted of Juan Cuadra and Blas Torrecillas (University of Almer´ ıa). The mem-
bers of the scientific committee were Nicol´ as Andruskiewitsch (National University
of ordoba, Argentina), Susan Montgomery (University of Southern California,
USA), Hans-J¨ urgen Schneider (University of Munich, Germany) and Freddy Van
Oystaeyen (University of Antwerp, Belgium). We would like to thank all partic-
ipants and speakers in the conference, who made possible such a successful and
fruitful event.
The conference was financed through various sources of the Spanish funding
for Education and Science. It had financial support from the Ministry of Science
and Innovation, the Andalusian Ministry of Economy, Science and Innovation, the
University of Almer´ ıa and its Faculty of Sciences, and the Algebra research group.
Several other institutions gave their support in some other ways: the department
of Algebra and Mathematical Analysis, the saving bank Cajamar, the city halls of
Almer´ ıa and ıjar and the county council of Almer´ ıa. The organizers are deeply
grateful to all of them.
The theory of Hopf algebras has widely evolved in many directions in the last
decade and new connections with other areas have come to surface. The talks in
the conference covered a large range of topics: classification of finite dimensional
Hopf algebras, with emphasis in the families of pointed and semisimple Hopf alge-
bras; Nichols algebras and Weyl groupoids; representations of Hopf algebras, espe-
cially of semisimple ones; representations of algebraic quantum groups; Hopf-Galois
theory; Hopf algebras in Combinatorics, homological properties of Hopf algebras,
Hopf algebra-like structures (quasi-Hopf algebras, weak Hopf algebras, etc.); tensor
categories, in particular fusion categories, and algebraic structures in them. The
contributions in these proceedings are a good sample of the topics discussed in the
conference. We briefly describe them. There is a survey by Dmitri Nikshych cover-
ing aspects on the classification of fusion categories through methods using Morita
equivalences. A long, self-contained, and comprehensive introduction to Hopf al-
gebras in the category of species is given by Aguiar and Mahajan. The paper by
Cohen and Westreich contains an original approach to semisimple Hopf algebras
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