Representation Theory of Artin Algebras
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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 a suitable introduction for any mathematician (especially graduate students) to this field. The main aim of the book is to illustrate how the theory of almost split sequences is used in the representation theory of Artin algebras. However, other foundational aspects of the subject are developed. These results giv...
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 a suitable introduction for any mathematician (especially graduate students) to this field. The main aim of the book is to illustrate how the theory of almost split sequences is used in the representation theory of Artin algebras. However, other foundational aspects of the subject are developed. These results give concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems, and numerous exercises.
Table of contents:
1. Artin rings; 2. Artin algebras; 3. Examples of algebras and modules; 4. The transpose and the dual; 5. Almost split sequences; 6. Finite representation type; 7. The Auslander-Reiten-quiver; 8. Hereditary algebras; 9. Short chains and cycles; 10. Stable equivalence; 11. Modules determining morphisms.
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 a suitable introduction for any mathematician (especially graduate students) to this field.
This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field.
Table of contents:
1. Artin rings; 2. Artin algebras; 3. Examples of algebras and modules; 4. The transpose and the dual; 5. Almost split sequences; 6. Finite representation type; 7. The Auslander-Reiten-quiver; 8. Hereditary algebras; 9. Short chains and cycles; 10. Stable equivalence; 11. Modules determining morphisms.
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 a suitable introduction for any mathematician (especially graduate students) to this field.
This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field.