Representations of Algebras: Tame and Wild Behavior

The book offers an original introduction to the representation theory of algebras, covering classical aspects of ring theory under new light with methods from linear algebra, categorical and homological methods, and notable results such as the Brauer–Thrall conjectures, Drozds theorem, and criteria to distinguish tame from wild algebras. It can serve as a basis for a second graduate course in algebra or as an introduction to research in the field.

Format: Paperback / softback
Length: 233 pages
Publication date: 24 October 2023
Publisher: Springer International Publishing AG

This book provides a unique introduction to the representation theory of algebras, catering to beginners in the field. It presents numerous results and techniques not typically found in introductory books, some of which are introduced here for the first time in book form. The exposition employs a combination of linear algebra methods (spectral methods and quadratic forms), categorical and homological methods (module categories, Galois coverings, Hochschild cohomology), and other techniques to provide fresh perspectives on classical ring theory. The book covers various topics, including rings with multiple objects, the Harada–Sai lemma, chain conditions, and Auslander–Reiten theory. Noteworthy and significant results covered in the book include the Brauer–Thrall conjectures, Drozds theorem, and criteria to distinguish tame algebras from wild algebras. This text can serve as the foundation for a second graduate course in algebra or as an introduction to research in the field of representation theory of algebras. Its originality and the breadth of topics covered make it a valuable resource for both beginners and established researchers in the field.

Dimension: 235 x 155 (mm)
ISBN-13: 9783031122903
Edition number: 1st ed. 2022