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The Resource Modular Representation Theory of Finite Groups, by Peter Schneider, (electronic resource)
Modular Representation Theory of Finite Groups, by Peter Schneider, (electronic resource)
Resource Information
The item Modular Representation Theory of Finite Groups, by Peter Schneider, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Modular Representation Theory of Finite Groups, by Peter Schneider, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 Representation theory studies maps from groups into the general linear group of a finitedimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory of finite groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the socalled 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its socalled 'defect group'. All these concepts are made explicit for the example of the special linear group of twobytwo matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely selfcontained
 Language
 eng
 Extent
 VIII, 178 p.
 Contents

 Prerequisites in module theory
 The Cartan{Brauer triangle
 The Brauer character
 Green's theory of indecomposable modules
 Blocks
 Isbn
 9781447148326
 Label
 Modular Representation Theory of Finite Groups
 Title
 Modular Representation Theory of Finite Groups
 Statement of responsibility
 by Peter Schneider
 Language
 eng
 Summary
 Representation theory studies maps from groups into the general linear group of a finitedimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular representation theory of finite groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the socalled 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its socalled 'defect group'. All these concepts are made explicit for the example of the special linear group of twobytwo matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely selfcontained
 http://library.link/vocab/creatorName
 Schneider, Peter
 Image bit depth
 0
 LC call number
 QA251.5
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Group theory
 Mathematics
 Associative Rings and Algebras
 Group Theory and Generalizations
 Label
 Modular Representation Theory of Finite Groups, by Peter Schneider, (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
 Prerequisites in module theory  The Cartan{Brauer triangle  The Brauer character  Green's theory of indecomposable modules  Blocks
 Dimensions
 unknown
 Extent
 VIII, 178 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9781447148326
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9781447148326
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9781447148326
 Label
 Modular Representation Theory of Finite Groups, by Peter Schneider, (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
 Prerequisites in module theory  The Cartan{Brauer triangle  The Brauer character  Green's theory of indecomposable modules  Blocks
 Dimensions
 unknown
 Extent
 VIII, 178 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9781447148326
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9781447148326
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9781447148326
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