Basic Representation Theory of Algebras. 1st ed. 2020

種類:

電子ブック

責任表示:

by Ibrahim Assem, Flávio U. Coelho

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Assem, Ibrahim.
• Coelho, Flávio U.
• SpringerLink (Online service)

シリーズ名:

Graduate Texts in Mathematics ; 283

ISBN:

9783030351182 [3030351181]    

注記:

Introduction -- Chapter 1: Modules, algebras and quivers -- Chapter 2: The radical and almost split sequences -- Chapter 3: Constructing almost split sequences -- Chapter 4: The Auslander–Reiten quiver of an algebra -- Chapter 5: Endomorphism algebras -- Chapter 6: Representation-finite algebras -- Bibliography -- Index.
This textbook introduces the representation theory of algebras by focusing on two of its most important aspects: the Auslander-Reiten theory and the study of the radical of a module category. It starts by introducing and describing several characterisations of the radical of a module category, then presents the central concepts of irreducible morphisms and almost split sequences, before providing the definition of the Auslander-Reiten quiver, which encodes much of the information on the module category. It then turns to the study of endomorphism algebras, leading on one hand to the definition of the Auslander algebra and on the other to tilting theory. The book ends with selected properties of representation-finite algebras, which are now the best understood class of algebras. Intended for graduate students in representation theory, this book is also of interest to any mathematician wanting to learn the fundamentals of this rapidly growing field. A graduate course in non-commutative or homological algebra, wh

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