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Algebras and Representation Theory


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Table of Contents

1 Introduction.- 2 Algebras.- 3 Modules and Representations.- 4 Simple Modules in the Jordan-Hoelder 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.

About the Author

Karin Erdmann's research focus lies on representation theory of finite groups, and finite-dimensional algebras. She has written many research articles, and is the author of a research monograph and a textbook.Thorsten Holm is Professor of Mathematics at Leibniz Universitat Hannover. His research interests include representation theory of finite groups and finite-dimensional algebras, and algebraic combinatorics.


"The book under review is a text-book for higher undergraduate mathematics students or graduate students who have previous knowledge of results from linear algebra, and basic properties of rings and groups. ... It is also useful for non-experts (in representation theory of quivers), they may benefit from this book in several ways: by examining the numerous worked examples, or by working out the many exercises." (Bin Zhu, zbMATH 1429.16001, 2020)

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