The Resource Modular Representation Theory of Finite Groups, by Peter Schneider, (electronic resource)

Modular Representation Theory of Finite Groups, by Peter Schneider, (electronic resource)

Label
Modular Representation Theory of Finite Groups
Title
Modular Representation Theory of Finite Groups
Statement of responsibility
by Peter Schneider
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
Representation theory studies maps from groups into the general linear group of a finite-dimensional 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 so-called '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 so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two 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 self-contained
http://library.link/vocab/creatorName
Schneider, Peter
Image bit depth
0
LC call number
QA251.5
Literary form
non fiction
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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)
Instantiates
Publication
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
10.1007/978-1-4471-4832-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-1-4471-4832-6
Label
Modular Representation Theory of Finite Groups, by Peter Schneider, (electronic resource)
Publication
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
10.1007/978-1-4471-4832-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-1-4471-4832-6

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