Triangulated categories in the representation theory of finite dimensional algebras /

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Bibliographic Details
Author / Creator:	Happel, Dieter, 1953-
Imprint:	Cambridge ; New York : Cambridge University Press, 1988.
Description:	1 online resource (208 pages).
Language:	English
Series:	London Mathematical Society lecture note series ; 119 London Mathematical Society lecture note series ; 119.
Subject:	Triangulated categories. Representations of algebras. Modules (Algebra) Modules (Algebra) Representations of algebras. Triangulated categories. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11181428

Hidden Bibliographic Details
ISBN:	9781107361362 1107361362 9780511892271 0511892276 0521339227 9780521339223 1139881760 9781139881760 1107366275 9781107366275 1107368448 9781107368446 1299404065 9781299404069 1107363810 9781107363816 0511629222 9780511629228
Notes:	Includes bibliographical references and index. English. Print version record.
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.
Other form:	Print version: Happel, Dieter, 1953- Triangulated categories in the representation theory of finite dimensional algebras. Cambridge ; New York : Cambridge University Press, 1988 0521339227

Table of 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

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