Representations of Algebras

Tame and Wild Behavior

José-Antonio de la Peña (Autor)

Buch | Hardcover

XIV, 233 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-12287-3 (ISBN)

Artikel merken

This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form. The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings with several objects, the Harada-Sai lemma, chain conditions, and Auslander-Reiten theory. Noteworthy and significant results covered in the book include the Brauer-Thrall conjectures, Drozd's theorem, and criteria to distinguish tame from wild algebras. This text may serve as the basis for a second graduate course in algebra or as an introduction to research in the field of representation theory of algebras. The originality of the exposition and the wealth of topics covered also make it a valuable resource for more established researchers.

Jose-Antonio de la Pena, born in Mexico in 1958, is a mathematician at the Universidad Autonoma de Mexico. An expert in algebra, he has published around 150 papers and has received several honors, notably membership of El Colegio Nacional (Mexico) since 2012.

1 Introduction and First Examples.- 2 A Categorical Approach.- 3 Constructive Methods.- 4 Spectral Methods in Representation Theory.- 5 Group Actions on Algebras and Module Categories.- 6 Reflections and Weyl Groups.- 7 Simply Connected Algebras.- 8 Degenerations of Algebras.- 9 Further Comments.

"This book fills an existing research gap through illuminating the paths towards technological innovation. ... this book provides valuable insights that inspire further research and offer a wealth of knowledge covering both theoretical underpinnings and practical illustrations of technological innovations in the context of wine tourism." (IokTeng Esther Kou, Information Technology & Tourism, Vol. 25 (3), 2023)

Erscheinungsdatum	25.10.2022
Reihe/Serie	Algebra and Applications
Zusatzinfo	XIV, 233 p. 1 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	496 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Auslander-Reiten theory • Brauer-Thrall conjectures • Coxeter transformations • Deformations of algebras • Drozd's dichotomy theorem • Galois coverings • quadratic forms • Representation Theory • Tame algebras • translation quivers • Wild algebras
ISBN-10	3-031-12287-9 / 3031122879
ISBN-13	978-3-031-12287-3 / 9783031122873
Zustand	Neuware