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Introduction to the representation theory of algebras [electronic resource]

Introduction to the representation theory of algebras [electronic resource]

자료유형
E-Book(소장)
개인저자
Barot, Michael.
서명 / 저자사항
Introduction to the representation theory of algebras [electronic resource] / Michael Barot.
발행사항
Cham :   Springer International Publishing :   Imprint: Springer,   2015.  
형태사항
1 online resource (x, 179 p.) : ill.
ISBN
9783319114750
요약
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.
일반주기
Title from e-Book title page.  
내용주기
Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.
서지주기
Includes bibliographical references and indexes.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Representations of algebras.
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245 1 0 ▼a Introduction to the representation theory of algebras ▼h [electronic resource] / ▼c Michael Barot.
260 ▼a Cham : ▼b Springer International Publishing : ▼b Imprint: Springer, ▼c 2015.
300 ▼a 1 online resource (x, 179 p.) : ▼b ill.
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and indexes.
505 0 ▼a Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.
520 ▼a 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Representations of algebras.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-319-11475-0
945 ▼a KLPA
991 ▼a E-Book(소장)

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