The Block Theory of Finite Group Algebras: Volume 1

The Block Theory of Finite Group Algebras: Volume 1

Author: Markus Linckelmann

Publisher: Cambridge University Press

Published: 2018-05-24

Total Pages: 0

ISBN-13: 9781108425919

DOWNLOAD EBOOK

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.


Book Synopsis The Block Theory of Finite Group Algebras: Volume 1 by : Markus Linckelmann

Download or read book The Block Theory of Finite Group Algebras: Volume 1 written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

The Block Theory of Finite Group Algebras

The Block Theory of Finite Group Algebras

Author: Markus Linckelmann

Publisher: Cambridge University Press

Published: 2018-05-24

Total Pages: 523

ISBN-13: 1108425909

DOWNLOAD EBOOK

A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.


Book Synopsis The Block Theory of Finite Group Algebras by : Markus Linckelmann

Download or read book The Block Theory of Finite Group Algebras written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of block theory, emphasising cornerstones of the area which have not appeared in any book before.

The Block Theory of Finite Group Algebras: Volume 1

The Block Theory of Finite Group Algebras: Volume 1

Author: Markus Linckelmann

Publisher: Cambridge University Press

Published: 2018-05-24

Total Pages: 527

ISBN-13: 1108575315

DOWNLOAD EBOOK

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.


Book Synopsis The Block Theory of Finite Group Algebras: Volume 1 by : Markus Linckelmann

Download or read book The Block Theory of Finite Group Algebras: Volume 1 written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

The Block Theory of Finite Group Algebras: Volume 2

The Block Theory of Finite Group Algebras: Volume 2

Author: Markus Linckelmann

Publisher: Cambridge University Press

Published: 2018-05-24

Total Pages: 523

ISBN-13: 1108562582

DOWNLOAD EBOOK

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.


Book Synopsis The Block Theory of Finite Group Algebras: Volume 2 by : Markus Linckelmann

Download or read book The Block Theory of Finite Group Algebras: Volume 2 written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

The Block Theory of Finite Group Algebras: Volume 2

The Block Theory of Finite Group Algebras: Volume 2

Author: Markus Linckelmann

Publisher: Cambridge University Press

Published: 2018-05-24

Total Pages: 0

ISBN-13: 9781108425902

DOWNLOAD EBOOK

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.


Book Synopsis The Block Theory of Finite Group Algebras: Volume 2 by : Markus Linckelmann

Download or read book The Block Theory of Finite Group Algebras: Volume 2 written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras

Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras

Author: D. J. Benson

Publisher: Cambridge University Press

Published: 1998-06-18

Total Pages: 260

ISBN-13: 9780521636537

DOWNLOAD EBOOK

An introduction to modern developments in the representation theory of finite groups and associative algebras.


Book Synopsis Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras by : D. J. Benson

Download or read book Representations and Cohomology: Volume 1, Basic Representation Theory of Finite Groups and Associative Algebras written by D. J. Benson and published by Cambridge University Press. This book was released on 1998-06-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to modern developments in the representation theory of finite groups and associative algebras.

A Course in Finite Group Representation Theory

A Course in Finite Group Representation Theory

Author: Peter Webb

Publisher: Cambridge University Press

Published: 2016-08-19

Total Pages: 339

ISBN-13: 1107162394

DOWNLOAD EBOOK

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.


Book Synopsis A Course in Finite Group Representation Theory by : Peter Webb

Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Characters and Blocks of Finite Groups

Characters and Blocks of Finite Groups

Author: Gabriel Navarro

Publisher: Cambridge University Press

Published: 1998-05-07

Total Pages: 301

ISBN-13: 0521595134

DOWNLOAD EBOOK

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.


Book Synopsis Characters and Blocks of Finite Groups by : Gabriel Navarro

Download or read book Characters and Blocks of Finite Groups written by Gabriel Navarro and published by Cambridge University Press. This book was released on 1998-05-07 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.

Representation Theory of Finite Groups: a Guidebook

Representation Theory of Finite Groups: a Guidebook

Author: David A. Craven

Publisher: Springer Nature

Published: 2019-08-30

Total Pages: 294

ISBN-13: 3030217922

DOWNLOAD EBOOK

This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.


Book Synopsis Representation Theory of Finite Groups: a Guidebook by : David A. Craven

Download or read book Representation Theory of Finite Groups: a Guidebook written by David A. Craven and published by Springer Nature. This book was released on 2019-08-30 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to the state of the art of representation theory of finite groups. Starting from a basic level that is summarized at the start, the book proceeds to cover topics of current research interest, including open problems and conjectures. The central themes of the book are block theory and module theory of group representations, which are comprehensively surveyed with a full bibliography. The individual chapters cover a range of topics within the subject, from blocks with cyclic defect groups to representations of symmetric groups. Assuming only modest background knowledge at the level of a first graduate course in algebra, this guidebook, intended for students taking first steps in the field, will also provide a reference for more experienced researchers. Although no proofs are included, end-of-chapter exercises make it suitable for student seminars.

Representation Theory of Finite Reductive Groups

Representation Theory of Finite Reductive Groups

Author: Marc Cabanes

Publisher: Cambridge University Press

Published: 2004-01-29

Total Pages: 457

ISBN-13: 0521825172

DOWNLOAD EBOOK

Publisher Description


Book Synopsis Representation Theory of Finite Reductive Groups by : Marc Cabanes

Download or read book Representation Theory of Finite Reductive Groups written by Marc Cabanes and published by Cambridge University Press. This book was released on 2004-01-29 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description