結合的代数の表現論（テキスト） Elements of the Representation Theory of Associative Algebras: Volume 1 : Techniques of Representation Theory (London Mathematical Society Student Texts)

Assem, Ibrahim/ Skowronski, Andrzej/ Simson, Daniel

Cambridge University Press（2006/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 472 p.
• 言語 ENG
• 商品コード 9780521584234
• DDC分類 512.24

Full Description

This first part of a two-volume set offers a modern account of the representation theory of finite dimensional associative algebras over an algebraically closed field. The authors present this topic from the perspective of linear representations of finite-oriented graphs (quivers) and homological algebra. The self-contained treatment constitutes an elementary, up-to-date introduction to the subject using, on the one hand, quiver-theoretical techniques and, on the other, tilting theory and integral quadratic forms. Key features include many illustrative examples, plus a large number of end-of-chapter exercises. The detailed proofs make this work suitable both for courses and seminars, and for self-study. The volume will be of great interest to graduate students beginning research in the representation theory of algebras and to mathematicians from other fields.

Contents

Introduction; 1. Algebras and modules; 2. Quivers and algebras; 3. Representations and modules; 4. Auslander-Reiten theory; 5. Nakayama algebras and representation-finite group algebras; 6. Tilting theory; 7. Representation-finite hereditary algebras; 8. Tilted algebras; 9. Directing modules and postprojective components; Appendix: categories, functors and homology.