EAN: 9783319114743

INTRODUCTION TO THE REPRESENTATION THEORY OF AL...

This book gives a general introduction to the theory of representations of algebras. It starts
with examples of classification problems of matrices under linear transformations  explaining
the three common setups: representation of quivers  modules over algebras and additive functors
over certain categories. The main part is devoted to (i) module categories  presenting the
unicity of the decomposition into indecomposable modules  the Auslander Reiten theory and the
technique of knitting  (ii) the use of combinatorial tools such as dimension vectors and
integral quadratic forms  and (iii) deeper theorems such as Gabriel s Theorem  the trichotomy
and the Theorem of Kac all accompanied by further examples. Each section includes exercises to
facilitate understanding. By keeping the proofs as basic and comprehensible as possible and
introducing the three languages at the beginning  this book is suitable for readers from the
advanced undergraduate level onwards and enables them to consult related  specific research
articles.

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