The Workshop on Representations of Algebras and Related Topics was held
in Queretaro, Mexico, from August 11 to 14, 2004, as a preliminary activity to
the 11th International Conference on Representations of Algebras that was held
at Patzcuaro, Mexico, the week after. More than 150 researchers and graduate
students participated in both the Workshop and the Conference.
It is a tradition in the area that previous to the main Conference a series
of courses and lectures are given on the topics that, in the opinion of the Or-
ganizing Committee, have marked new trends in the theory or that present new
possibilities of interaction with other mathematical topics. The topics selected for
this Workshop were the following: Algebraic deformation theory (Ragnar Buch-
weitz, U. Toronto, Canada), Quantum subgroups and canonical basis for quantum
Lie groups (Adrian Ocneanu, Penn State U., United States), The Gabriel-Roiter
measure (Claus M. Ringel, U. Bielefeld, Germany), Categorifications and derived
categories (Raphael Rouquier, U. Paris 7, France), Selfinjective algebras: finite and
tame type (Andrzej Skowronski, U. Torun, Poland), Support varieties for modules
and complexes (0eyvind Solberg, U. Trondheim, Norway), Cluster algebras (Andrei
Zelevinsky, Northeastern U., United States).
The topics presented at the Workshop are not the only subjects deserving spe-
cial attention by researchers in the Representation Theory field. After the Confer-
ence, we asked some mathematicians to prepare survey articles on other topics not
presented at the Workshop. This Proceedings volume is the result of this double
effort: some of the papers are based on the lectures at the Workshop, and others
are specially prepared for this volume. We think the volume gives an original, fair
presentation of the main trends of the subject, addressed not only to specialists but
to a broader audience.
We express our gratitude to all authors contributing to this volume and the
referees for their assistance.
We thank Teresa Hernandez for her technical support before and during the
Workshop and for the preparation of this volume. We thank Christine Thivierge of
the AMS staff for her efficient support and help in the preparation of this Proceed-
ings. We are glad that the Proceedings of our Workshop appear in the Contempo-
rary Mathematics series of the American Mathematical Society.
Jose A. de la Peiia and Raymundo Bautista,
Mexico, December 2005