Elements of the Representation Theory of Associative Algebras: Volume 3, Representation-infinite Tilted AlgebrasThe final part of a three-volume set providing a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The subject is presented from the perspective of linear representations of quivers and homological algebra. This volume provides an introduction to the representation theory of representation-infinite tilted algebras from the point of view of the time-wild dichotomy. Also included is a collection of selected results relating to the material discussed in all three volumes. The book is primarily addressed to a graduate student starting research in the representation theory of algebras, but will also be of interest to mathematicians in other fields. Proofs are presented in complete detail, and the text includes many illustrative examples and a large number of exercises at the end of each chapter, making the book suitable for courses, seminars, and self-study. |
Contents
XVI | 65 |
78 | 100 |
Wild hereditary algebras and tilted algebras | 213 |
Copyright | |
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Elements of the Representation Theory of Associative Algebras: Volume 3 ... Daniel Simson,Andrzej Skowronski No preview available - 2007 |
Common terms and phrases
algebra of Euclidean Assume Auslander-Reiten quiver mod brick canonical algebra concealed algebra contains defined dimê dimension vectors direct sum direct summands Dynkin epimorphism equivalence of categories Euclidean type Euler quadratic form exact sequence exists faithful finishes the proof finite dimensional K-algebra generalised standard Grothendieck group Hence HomA HomA(T homomorphism I(mod indecomposable injective indecomposable modules indecomposable projective injective module integer K-algebra K-linear functor Ko(A Ko(B Math modules in mod monomorphism Moreover morphism P₁(K)-family pairwise non-isomorphic pairwise orthogonal standard path algebra postprojective component preinjective component projective module prove quadratic form quasi-simple regular quasitilted algebras quiver Q quotient algebra regular A-module regular component repk representation embedding representation theory representation type representation-infinite representation-tame selfinjective algebras simple module Skowroński split sequence standard stable tubes subcategory T(mod T₁ tilting A-module torsion tubular type unique vertex wild hereditary algebra wild quiver