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Trends in Representation Theory of Algebras and Related Topics
EMS Series of Congress Reports

Trends in Representation Theory of Algebras and Related Topics

Andrzej Skowroński (Nicolaus Copernicus University, Toruń, Poland)

ISBN print 978-3-03719-062-3, ISBN online 978-3-03719-562-8
DOI 10.4171/062
September 2008, 722 pages, hardcover, 17 x 24 cm.
98.00 Euro

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, model theory.

The 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.

Further Information

Review in MR 2490402 (2009j:16001)

Review in Zentralblatt MATH 1144.16003

EMS Review