The Resource Introduction to the Representation Theory of Algebras, by Michael Barot, (electronic resource)
Introduction to the Representation Theory of Algebras, by Michael Barot, (electronic resource)
Resource Information
The item Introduction to the Representation Theory of Algebras, by Michael Barot, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Introduction to the Representation Theory of Algebras, by Michael Barot, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 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 AuslanderReiten 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
 Language
 eng
 Extent
 X, 179 p. 109 illus.
 Contents

 Matrix Problems
 Representations of Quivers
 Algebras
 Module Categories
 Elements of Homological Algebra
 The AuslanderReiten Theory
 Knitting
 Combinatorial Invariants
 Indecomposables and Dimensions
 Isbn
 9783319114750
 Label
 Introduction to the Representation Theory of Algebras
 Title
 Introduction to the Representation Theory of Algebras
 Statement of responsibility
 by Michael Barot
 Language
 eng
 Summary
 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 AuslanderReiten 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
 http://library.link/vocab/creatorName
 Barot, Michael
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink (Online service)
 http://library.link/vocab/subjectName

 Mathematics
 Associative rings
 Rings (Algebra)
 Category theory (Mathematics)
 Homological algebra
 Algebra
 Label
 Introduction to the Representation Theory of Algebras, by Michael Barot, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Matrix Problems  Representations of Quivers  Algebras  Module Categories  Elements of Homological Algebra  The AuslanderReiten Theory  Knitting  Combinatorial Invariants  Indecomposables and Dimensions
 Control code
 9783319114750
 Dimensions
 unknown
 Extent
 X, 179 p. 109 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319114750
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319114750
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086491726
 Label
 Introduction to the Representation Theory of Algebras, by Michael Barot, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 Matrix Problems  Representations of Quivers  Algebras  Module Categories  Elements of Homological Algebra  The AuslanderReiten Theory  Knitting  Combinatorial Invariants  Indecomposables and Dimensions
 Control code
 9783319114750
 Dimensions
 unknown
 Extent
 X, 179 p. 109 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319114750
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319114750
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086491726
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/IntroductiontotheRepresentationTheoryof/6EC3yJkTILU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/IntroductiontotheRepresentationTheoryof/6EC3yJkTILU/">Introduction to the Representation Theory of Algebras, by Michael Barot, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>