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E-book
Author Happel, Dieter, 1953-

Title Triangulated categories in the representation theory of finite dimensional algebras / Dieter Happel
Published Cambridge ; New York : Cambridge University Press, 1988

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Description 1 online resource (208 pages)
Series London Mathematical Society lecture note series ; 119
London Mathematical Society lecture note series ; 119.
Contents Cover; Title; Copyright; Contents; Preface; CHAPTER I: Triangulated categories; 1. Foundations; 2. Frobenius categories; 3. Examples; 4. Auslander-Reiten triangles; 5. Description of some derived categories; CHAPTER II: Repetitive algebras; 1. t-categories; 2. Repetitive algebras; 3. Generating subcategories; 4. The main theorem; 5. Examples; CHAPTER III: Tilting theory; 1. Grothendieck groups of triangulated categories; 2. The invariance property; 3. The Brenner-Butler Theorem; 4. Torsion theories; 5. Tilted algebras; 6. Partial tilting modules; 7. Concealed algebras
CHAPTER IV: Piecewise hereditary algebras1. Piecewise hereditary algebras; 2. Cycles in mod kZ?; 3. The representation-finite case; 4. Iterated tilted algebras; 5. The general case; 6. The Dynkin case; 7. The affine case; CHAPTER V: Trivial extension algebras; 1. Preliminaries; 2. The representation-finite case; 3. The representation-infinite case; References; Index
Summary This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras
Bibliography Includes bibliographical references and index
Notes English
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Subject Triangulated categories.
Representations of algebras.
Modules (Algebra)
Categories (Mathematics)
MATHEMATICS -- Algebra -- Linear.
Categories (Mathematics)
Modules (Algebra)
Representations of algebras
Triangulated categories
Algebra
Darstellungstheorie
Dimension n
Kategorie Mathematik
Triangulation
Categorieën (wiskunde)
Associatieve ringen.
Algebra associativa.
Algebra homologica.
Représentations d'algèbres.
Modules (algèbre)
Catégories (mathématiques)
Form Electronic book
ISBN 9781107361362
1107361362
9780511892271
0511892276
1139881760
9781139881760
1107366275
9781107366275
1107368448
9781107368446
1299404065
9781299404069
1107363810
9781107363816
0511629222
9780511629228