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Trends in Representation Theory of Algebras and Related Topics
Edited by: Andrzej Skowroński, Nicolaus Copernicus University, Torun, Poland
A publication of the European Mathematical Society.
EMS Series of Congress Reports
2008; 722 pp; hardcover
Volume: 1
ISBN-10: 3-03719-062-0
ISBN-13: 978-3-03719-062-3
List Price: US$138
Member Price: US$110.40
Order Code: EMSSCR/1
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This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development.

The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincaré duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory.

This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.


Graduate students and research mathematicians interested in representation theory.

Table of Contents

  • S. Ariki -- Finite dimensional Hecke algebras
  • G. Bobiński, C. Riedtmann, and A. Skowroński -- Semi-invariants of quivers and their zero sets
  • I. Burban and Y. Drozd -- Maximal Cohen-Macaulay modules over surface singularities
  • J. F. Carlson -- Rank varieties
  • K. Erdmann and A. Skowroński -- Periodic algebras
  • C. Geiss, B. Leclerc, and J. Schröer -- Preprojective algebras and cluster algebras
  • I. G. Gordon -- Symplectic reflection algebras
  • O. Iyama -- Auslander-Reiten theory revisited
  • P. Jørgensen -- Calabi-Yau categories and Poincaré duality spaces
  • S. Kasjan -- Representation types of algebras from the model theory point of view
  • B. Keller -- Calabi-Yau triangulated categories
  • S. Koenig -- A panorama of diagram algebras
  • H. Lenzing and J. A. de la Peńa -- Spectral analysis of finite dimensional algebras and singularities
  • M. Reineke -- Moduli of representations of quivers
  • A. Skowroński and K. Yamagata -- Selfinjective algebras of quasitilted type
  • List of contributors
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