Introduction to the Representation Theory of Algebras

Michael Barot was a researcher at the Instituto de Matemáticas of the Universidad Nacional Autónoma de México.

• Matrix Problems.- Representations of Quivers.- Algebras.- Module Categories.- Elements of Homological Algebra.- The Auslander-Reiten Theory.- Knitting.- Combinatorial Invariants.- Indecomposables and Dimensions.

"This book is a short and elementary course in the representation theory of finite dimensional algebras. It may be a good text book for undergraduate and PhD students, because only the knowledge of linear algebra is required." (Justyna Kosakowska, zbMATH 1330.16001, 2016) "Barot (former researcher, Instituto de Matematicas, Univ. Nacional Autonoma de Mexico) paints the big picture and emphasizes recent perspectives. ... An advanced undergraduate could read this book as a wonderful case study in the power of shifting viewpoints and thus an initiation into the modern practice of mathematics. ... Summing Up: Highly recommended. Lower- and upper-division undergraduates, graduate students, researchers/faculty, and professionals/practitioners." (D. V. Feldman, Choice, Vol. 53 (4), December, 2015) "The book gives a first introduction to the representation theory of finite-dimensional algebras over an algebraically closed field. ... With its well-chosen topics, arranged in a smooth and attractive order, the book is highly recommended as a one-semester introductory course on representations of finite-dimensional algebras." (Wolfgang Rump, Mathematical Reviews, October, 2015)