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Introduction to the Representation Theory of Algebras
Angielski
127 b
30 dni na zwrot towaru
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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 common three different 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 (e.g. 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.§By maintaining the proofs as basic and comprehensible as possible, and with developing 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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Angielski
