東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Basic representation theory of algebras

Assem, Ibrahim.

Linked to FindBook

Google Book

Amazon

博客來

Basic representation theory of algebras

Record Type:	Electronic resources : Monograph/item
Title/Author:	Basic representation theory of algebras/ by 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.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Representations of algebras. -
Online resource:	https://doi.org/10.1007/978-3-030-35118-2
ISBN:	9783030351182

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 ;283..

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

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

572480
Representations of algebras.

LC Class. No.: QA155 / .A874 2020

Dewey Class. No.: 512.2

Basic representation theory of algebras
LDR:02459nmm a2200337 a 4500 001 2217240
003 DE-He213
005 20200806114822.0
006 m d
007 cr nn 008maaau
008 201120s2020 sz s 0 eng d
020 $a 9783030351182 $q (electronic bk.)
020 $a 9783030351175 $q (paper)
024 7 $a 10.1007/978-3-030-35118-2 $2 doi
035 $a 978-3-030-35118-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA155 $b .A874 2020
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.2 $2 23
090 $a QA155 $b .A844 2020
100 1 $a Assem, Ibrahim. $3 629843
245 1 0 $a Basic representation theory of algebras $h [electronic resource] / $c by Ibrahim Assem, Flavio U. Coelho.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a x, 311 p. : $b ill., digital ; $c 24 cm.
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 572480
650 1 4 $a Associative Rings and Algebras. $3 897405
650 2 4 $a Category Theory, Homological Algebra. $3 899944
700 1 $a Coelho, Flavio U. $3 3450330
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Graduate texts in mathematics ; $v 283. $3 3450331
856 4 0 $u https://doi.org/10.1007/978-3-030-35118-2
950 $a Mathematics and Statistics (Springer-11649)