Algebras and Representation Theory

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 Universität 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)

• 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.