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Author: Maurice Auslander
Publisher: Cambridge University Press
ISBN: 9780521599238
Category : Mathematics
Languages : en
Pages : 444
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Book Description
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
Author: Maurice Auslander
Publisher: Cambridge University Press
ISBN: 9780521599238
Category : Mathematics
Languages : en
Pages : 444
Get Book Here
Book Description
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
Author: Maurice Auslander
Publisher:
ISBN:
Category : Artin algebras
Languages : en
Pages : 179
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Book Description
Author: Idun Reiten
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
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Book Description
Author: Karin Erdmann
Publisher: Springer
ISBN: 3319919989
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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.
Author: Maurice Auslander
Publisher: American Mathematical Soc.
ISBN: 9780821809983
Category : Mathematics
Languages : en
Pages : 924
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Book Description
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.
Author: Henning Krause
Publisher: Cambridge University Press
ISBN: 1108985815
Category : Mathematics
Languages : en
Pages : 518
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Book Description
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.
Author: M. Auslander
Publisher: Springer
ISBN: 3540393137
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Author: A. Martsinkovsky
Publisher: Cambridge University Press
ISBN: 9780521577892
Category : Mathematics
Languages : en
Pages : 148
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Book Description
For any researcher working in representation theory, algebraic or arithmetic geometry.
Author: M. Auslander
Publisher: Springer
ISBN: 3540389636
Category : Mathematics
Languages : en
Pages : 391
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Book Description
Author: Pavel I. Etingof
Publisher: American Mathematical Soc.
ISBN: 0821853511
Category : Mathematics
Languages : en
Pages : 240
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Book Description
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
