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Algebras and representation theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Algebras and representation theory/ by Karin Erdmann, Thorsten Holm.
作者:	Erdmann, Karin.
其他作者:	Holm, Thorsten.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	ix, 298 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Representations of algebras. -
電子資源:	https://doi.org/10.1007/978-3-319-91998-0
ISBN:	9783319919980

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

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

902229
Representations of algebras.

LC Class. No.: QA155 / .E736 2018

Dewey Class. No.: 512.2

Algebras and representation theory
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245 1 0 $a Algebras and representation theory $h [electronic resource] / $c by Karin Erdmann, Thorsten Holm.
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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 902229
650 1 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Commutative Rings and Algebras. $3 672054
650 2 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Category Theory, Homological Algebra. $3 678397
700 1 $a Holm, Thorsten. $3 1208761
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