Algebras and Representation Theory

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-Hölder theorem on composition series, the Art...

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Bibliographic Details
Main Author: Erdmann, Karin (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:1st ed. 2018.
Series:Springer Undergraduate Mathematics Series,
Subjects:
Associative rings.
Rings (Algebra).
Commutative algebra.
Commutative rings.
Group theory.
Category theory (Mathematics).
Homological algebra.
ISBN:9783319919980
ISSN:1615-2085
Online Access: Get full text
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Table of Contents:
  • 1 Introduction
  • 2 Algebras
  • 3 Modules and Representations
  • 4 Simple Modules in the Jordan-Hölder 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.

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