LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	512.46
Title	Introduction to the Representation Theory of Algebras ([EBook]) / by Michael Barot.
Author	Barot, Michael
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2015.
Physical Details	X, 179 p. 109 illus. : online resource.
ISBN	9783319114750
Summary Note	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 and explains 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.:
Contents note	Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-11475-0
Links to Related Works	Subject References: Algebra . Associative rings . Associative Rings and Algebras . Category Theory, Homological Algebra . Category theory (Mathematics) . General Algebraic Systems . Homological algebra . Mathematics . Rings (Algebra) . Authors: Barot, Michael . Corporate Authors: SpringerLink (Online service) . Classification: 512.46 .

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Introduction to the Representation Theory of Algebras

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