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Basic representation theory of algebras

Assem, Ibrahim.

Basic representation theory of algebras

Record Type:	Electronic resources : Monograph/item
Title/Author:	Basic representation theory of algebrasby Ibrahim Assem, Flavio U. Coelho.
Author:	Assem, Ibrahim.
other author:	Coelho, Flavio U.
Published:	Cham :Springer International Publishing :2020.
Description:	x, 311 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Representations of algebras.
Online resource:	https://doi.org/10.1007/978-3-030-35118-2
ISBN:	9783030351182$q(electronic bk.)

Basic representation theory of algebras
Assem, Ibrahim.

Basic representation theory of algebras[electronic resource] /by Ibrahim Assem, Flavio U. Coelho. - Cham :Springer International Publishing :2020. - x, 311 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2830072-5285 ;. - Graduate texts in mathematics ;129..

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.

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.

ISBN: 9783030351182$q(electronic bk.)

Standard No.: 10.1007/978-3-030-35118-2doiSubjects--Topical Terms:

191077
Representations of algebras.

LC Class. No.: QA155 / .A874 2020

Dewey Class. No.: 512.2

Basic representation theory of algebras
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245 1 0 $a Basic representation theory of algebras $h [electronic resource] / $c by Ibrahim Assem, Flavio U. Coelho.
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490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 283
505 0 $a 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.
520 $a 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.
650 0 $a Representations of algebras. $3 191077
650 1 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Category Theory, Homological Algebra. $3 275954
700 1 $a Coelho, Flavio U. $3 860041
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773 0 $t Springer eBooks
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u https://doi.org/10.1007/978-3-030-35118-2
950 $a Mathematics and Statistics (Springer-11649)