Basic representation theory of algebras / Ibrahim Assem, Flávio U. Coelho.

Format:

Book

Author/Creator:

Assem, Ibrahim, author.

Coelho, Flávio Ulhoa, author.

Series:

Graduate texts in mathematics ; 0072-5285 283.

Graduate texts in mathematics, 0072-5285 ; 283

Language:

English

Subjects (All):

Representations of algebras.

Associative rings.

Modules (Algebra).

Algebra.

Physical Description:

x, 311 pages : illustrations ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2020]

Summary:

"This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander-Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, which is standard in most universities, is a prerequisite for readers of this book"--Provided by publisher.

Contents:

Introduction

Chapter 1. Modules, algebras and quivers

Chapter 2. The radical and almost split sequences

Chapter 3. Constructing almost split sequences

Chapter 4. The Auslander-Reiten quiver of an algebra

Chapter 5. Endomorphism algebras

Chapter 6. Representation-finite algebras

Bibliography

Index.

Notes:

Includes bibliographical references (pages 305-307) and index.

ISBN:

9783030351175

3030351173

OCLC:

1122912235

Publisher Number:

10.1007/3-030-35118-2