Triangulated categories in the representation theory of finite dimensional algebras / Dieter Happel.

Format:

Book

Author/Creator:

Happel, Dieter, 1953- author.

Series:

London Mathematical Society lecture note series ; 119.

London Mathematical Society lecture note series ; 119

Language:

English

Subjects (All):

Triangulated categories.

Representations of algebras.

Modules (Algebra).

Physical Description:

1 online resource (208 pages.) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1988.

Language Note:

English

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.

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

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88176-0

1-107-36627-5

1-107-37099-X

1-107-36136-2

1-107-36844-8

1-299-40406-5

1-107-36381-0

0-511-89227-6

0-511-62922-2