Representation Theory of Artin Algebras
Representation Theory of Artin Algebras

Author: Maurice Auslander

Publisher: Cambridge University Press

Published: 1997-08-21

Total Pages: 444

ISBN-13: 9780521599238

DOWNLOAD EBOOK

This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely self-contained, so the book is suitable for any mathematicians (especially graduate students) wanting an introduction to this active field.'...written in a clear comprehensive style with full proofs. It can very well serve as an excellent reference as well as a textbook for graduate students.' EMS Newletter

Algebras and Representation Theory
Algebras and Representation Theory

Author: Karin Erdmann

Publisher: Springer

Published: 2018-09-07

Total Pages: 304

ISBN-13: 3319919989

DOWNLOAD EBOOK

This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.

Selected Works of Maurice Auslander
Selected Works of Maurice Auslander

Author: Maurice Auslander

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 924

ISBN-13: 9780821809983

DOWNLOAD EBOOK

Auslander made contributions to many parts of algebra, and this 2-volume set (the set ISBN is 0-8218-0679-3, already published) contains a selection of his main work.

Homological Theory of Representations
Homological Theory of Representations

Author: Henning Krause

Publisher: Cambridge University Press

Published: 2021-11-18

Total Pages: 518

ISBN-13: 1108985815

DOWNLOAD EBOOK

Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library.

Representation Theory of Algebras and Related Topics
Representation Theory of Algebras and Related Topics

Author: Raymundo Bautista

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 428

ISBN-13: 9780821803967

DOWNLOAD EBOOK

These proceedings report a number of lecture series delivered during the Workshop on Representation Theory of Algebras and Related Topics held at Universidad Nacional Autonoma de Mexico (UNAM) in August 1994. The workshop was dedicated to recent advances in the field and its interaction with other areas of mathematics, such as algebraic geometry, ring theory, and representation of groups. The program of the Workshop consisted of 9 lecture series. In addition there was a Tame Day consisting of 6 lectures reporting on the recent advances in the study of tame algebras and their module categories. During the Workshop there was a session devoted to the exhibition of computer programs developed by participants. These programs are implementations of algorithms related to the calculation of important aspects of algebras and their module categories.