Elements of the Representation Theory of Associative Algebras, Vol 1: Techniques

Ibrahim Assem, Andrzej Skowronski, Daniel Simson, "Elements of the Representation Theory of Associative Algebras, Vol 1: Techniques of Representation Theory"

Cambridge University Press | 2006-02-13 | ISBN: 0521586313 | 468 pages | PDF | 3,5 MB

This first part of a three-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.

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