The Block Theory Of Finite Group Algebras Volume 2
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The Block Theory Of Finite Group Algebras Volume 2
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Author : Markus Linckelmann
language : en
Publisher: Cambridge University Press
Release Date : 2018-05-24
The Block Theory Of Finite Group Algebras Volume 2 written by Markus Linckelmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-24 with Mathematics categories.
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 1
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Author : Markus Linckelmann
language : en
Publisher: Cambridge University Press
Release Date : 2018-05-24
The Block Theory Of Finite Group Algebras Volume 1 written by Markus Linckelmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-24 with Mathematics categories.
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
DOWNLOAD
Author : Markus Linckelmann
language : en
Publisher: Cambridge University Press
Release Date : 2018-05-24
The Block Theory Of Finite Group Algebras written by Markus Linckelmann and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-24 with Mathematics categories.
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.
A Course In Finite Group Representation Theory
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Author : Peter Webb
language : en
Publisher: Cambridge University Press
Release Date : 2016-08-19
A Course In Finite Group Representation Theory written by Peter Webb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.
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.
Representation Theory Of Finite Groups A Guidebook
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Author : David A. Craven
language : en
Publisher: Springer Nature
Release Date : 2019-08-30
Representation Theory Of Finite Groups A Guidebook written by David A. Craven and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-30 with Mathematics categories.
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.
Groups 93 Galway St Andrews Volume 2
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Author : C. M. Campbell
language : en
Publisher: Cambridge University Press
Release Date : 1995-03-16
Groups 93 Galway St Andrews Volume 2 written by C. M. Campbell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-16 with Mathematics categories.
This two-volume book contains selected papers from the international conference 'Groups 1993 Galway / St Andrews' which was held at University College Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes. As with the Proceedings of the earlier 'Groups-St Andrews' conferences it is hoped that the articles in these Proceedings will, with their many references, prove valuable both to experienced researchers and also to new postgraduates interested in group theory.
Geometric Group Theory Volume 2
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Author : Graham A. Niblo
language : en
Publisher: Cambridge University Press
Release Date : 1993-08-12
Geometric Group Theory Volume 2 written by Graham A. Niblo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-12 with Mathematics categories.
The articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. This second volume contains solely a ground breaking paper by Gromov, which provides a fascinating look at finitely generated groups. For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.
Characters And Blocks Of Finite Groups
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Author : Gabriel Navarro
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-07
Characters And Blocks Of Finite Groups written by Gabriel Navarro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-07 with Mathematics categories.
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.
Topics In Symbolic Dynamics And Applications
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Author : F. Blanchard
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-29
Topics In Symbolic Dynamics And Applications written by F. Blanchard and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-29 with Mathematics categories.
This book is devoted to recent developments in symbolic dynamics, and it comprises eight chapters. The first two are concerned with the study of symbolic sequences of 'low complexity', the following two introduce 'high complexity' systems. The later chapters go on to deal with more specialised topics including ergodic theory, number theory, and one-dimensional dynamics.
Spectral Asymptotics In The Semi Classical Limit
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Author : Mouez Dimassi
language : en
Publisher: Cambridge University Press
Release Date : 1999-09-16
Spectral Asymptotics In The Semi Classical Limit written by Mouez Dimassi and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-16 with Mathematics categories.
Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be (and has been) covered in a one semester course.