Trends in Representation Theory of Algebras and Related TopicsThis 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, Poincare 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. |
Contents
Semiinvariants of quivers and their zero sets | 49 |
Maximal CohenMacaulay modules over surface singularities | 101 |
Rank varieties | 167 |
Periodic algebras | 201 |
Preprojective algebras and cluster algebras | 248 |
Symplectic reflection algebras | 285 |
AuslanderReiten theory revisited | 349 |
CalabiYau categories and Poincaré duality spaces | 399 |
Representation types of algebras from the model theory point of view | 433 |
CalabiYau triangulated categories | 467 |
A panorama of diagram algebras | 491 |
Spectral analysis of finite dimensional algebras and singularities | 541 |
Moduli of representations of quivers | 589 |
Selfinjective algebras of quasitilted type | 639 |
List of contributors | 709 |
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Trends in Representation Theory of Algebras and Related Topics Andrzej Skowroński No preview available - 2008 |
Common terms and phrases
A-module abelian affine algebraically closed field Amer Auslander Auslander-Reiten quiver automorphism Brauer algebras canonical algebra cluster algebras CM(A Cohen-Macaulay modules cohomology commutative complex reflection groups components Corollary Coxeter polynomial decomposition defined definition deformation denote derived category derived equivalent diagram algebras dimension vector duality Dynkin type elements exact sequence example extension algebra finite dimensional algebras finite group finite representation type functor Gorenstein graph group algebra Hecke algebras Hence Hochschild ideal indecomposable injective algebra integer irreducible isomorphism Jordan type K-algebra Krull dimension Lemma Math Mathematics matrix Moreover morphism n-cluster tilting Noetherian path algebra preprojective algebras projective proof Proposition quasitilted quotient rank variety representation theory result ring Section selfinjective algebras semi-invariants semisimple Skowroński space structure subcategory symmetric algebra symmetric groups symplectic reflection algebras Temperley-Lieb algebras tilted algebra tilting object triangle triangulated category vertices