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...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2018, 2018
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| Edition: | 1st ed. 2018 |
| Series: | Springer Undergraduate Mathematics Series
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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