國立高雄大學圖資館 |

Language: English

Back

Algebras and representation theory

Erdmann, Karin.

Algebras and representation theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebras and representation theoryby Karin Erdmann, Thorsten Holm.
Author:	Erdmann, Karin.
other author:	Holm, Thorsten.
Published:	Cham :Springer International Publishing :2018.
Description:	ix, 298 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Representations of algebras.
Online resource:	https://doi.org/10.1007/978-3-319-91998-0
ISBN:	9783319919980$q(electronic bk.)

Algebras and representation theory
Erdmann, Karin.

Algebras and representation theory[electronic resource] /by Karin Erdmann, Thorsten Holm. - Cham :Springer International Publishing :2018. - ix, 298 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

1 Introduction -- 2 Algebras -- 3 Modules and Representations -- 4 Simple Modules in the Jordan-Holder Theorem -- 5 Semisimple Modules and Semisimple Algebras -- 6 The Structure of Semisimple ALgebras - The Artin-Wedderburn Theorem -- 7 Semisimple Group Algebras and Maschke's Theorem -- 8 Indecomposable Modules -- 9 Representation Type -- 10 Representations of Quivers -- 11 Diagrams and Roots -- 12 Gabriel's Theorem -- 13 Proofs and Background -- 14 Appendix A: Induced Modules for Group Algebras -- 15 Appendix B: Solutions to Selected Exercises -- Index.

This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Holder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

ISBN: 9783319919980$q(electronic bk.)

Standard No.: 10.1007/978-3-319-91998-0doiSubjects--Topical Terms:

191077
Representations of algebras.

LC Class. No.: QA155 / .E736 2018

Dewey Class. No.: 512.2

Algebras and representation theory
LDR:02594nmm a2200337 a 4500 001 544004
003 DE-He213
005 20190304135354.0
006 m d
007 cr nn 008maaau
008 190430s2018 gw s 0 eng d
020 $a 9783319919980$q(electronic bk.)
020 $a 9783319919973$q(paper)
024 7 $a 10.1007/978-3-319-91998-0 $2 doi
035 $a 978-3-319-91998-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA155 $b .E736 2018
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 .E66 2018
100 1 $a Erdmann, Karin. $3 261425
245 1 0 $a Algebras and representation theory $h [electronic resource] / $c by Karin Erdmann, Thorsten Holm.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a ix, 298 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer undergraduate mathematics series, $x 1615-2085
505 0 $a 1 Introduction -- 2 Algebras -- 3 Modules and Representations -- 4 Simple Modules in the Jordan-Holder Theorem -- 5 Semisimple Modules and Semisimple Algebras -- 6 The Structure of Semisimple ALgebras - The Artin-Wedderburn Theorem -- 7 Semisimple Group Algebras and Maschke's Theorem -- 8 Indecomposable Modules -- 9 Representation Type -- 10 Representations of Quivers -- 11 Diagrams and Roots -- 12 Gabriel's Theorem -- 13 Proofs and Background -- 14 Appendix A: Induced Modules for Group Algebras -- 15 Appendix B: Solutions to Selected Exercises -- Index.
520 $a This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Holder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.
650 0 $a Representations of algebras. $3 191077
650 1 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Category Theory, Homological Algebra. $3 275954
700 1 $a Holm, Thorsten. $3 822451
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer undergraduate mathematics series. $3 544774
856 4 0 $u https://doi.org/10.1007/978-3-319-91998-0
950 $a Mathematics and Statistics (Springer-11649)