Techniques of representation theory
著者
書誌事項
Techniques of representation theory
（London Mathematical Society student texts, 65 . Elements of the representation theory of associative algebras ; v. 1）
Cambridge University Press, 2006
- : hardback
- : pbk
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注記
Includes bibliographical reference (p. 437-449) and indexes
内容説明・目次
内容説明
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.
目次
- 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.
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