Representation Theory of Artin Algebras

ISBN-13: 9780521599238 / Angielski / Miękka / 1997 / 440 str.

Maurice Auslander; B. Bollobas; W. Fulton

Opis

This book serves as a comprehensive introduction to the representation theory of Artin algebras, a branch of algebra. Written by three distinguished mathematicians, it illustrates how the theory of almost split sequences is utilized within representation theory. The authors develop several foundational aspects of the subject. For example, the representations of quivers with relations and their interpretation as modules over the factors of path algebras is discussed in detail. Thorough discussions yield concrete illustrations of some of the more abstract concepts and theorems. The book includes complete proofs of all theorems and numerous exercises. It is an invaluable resource for graduate students and researchers.

Recenzje

'... 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

Spis treści

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.