Representations Of Solvable Groups
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Representations Of Solvable Groups
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Author : Olaf Manz
language : en
Publisher: Cambridge University Press
Release Date : 1993-09-16
Representations Of Solvable Groups written by Olaf Manz 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 1993-09-16 with Mathematics categories.
Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer.
Representations Of Solvable Lie Groups
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Author : Didier Arnal
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-08
Representations Of Solvable Lie Groups written by Didier Arnal 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 2020-04-08 with Mathematics categories.
The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.
Representations Of Groups
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Author : Klaus Lux
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-01
Representations Of Groups written by Klaus Lux 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 2010-07-01 with Mathematics categories.
The representation theory of finite groups has seen rapid growth in recent years with the development of efficient algorithms and computer algebra systems. This is the first book to provide an introduction to the ordinary and modular representation theory of finite groups with special emphasis on the computational aspects of the subject. Evolving from courses taught at Aachen University, this well-paced text is ideal for graduate-level study. The authors provide over 200 exercises, both theoretical and computational, and include worked examples using the computer algebra system GAP. These make the abstract theory tangible and engage students in real hands-on work. GAP is freely available from www.gap-system.org and readers can download source code and solutions to selected exercises from the book's web page.
Characters And Blocks Of Solvable Groups
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Author : James Cossey
language : en
Publisher: Springer Nature
Release Date : 2024-04-12
Characters And Blocks Of Solvable Groups written by James Cossey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-12 with Mathematics categories.
This book highlights recent developments in the representation theory of finite solvable groups, which seeks to connect group theory to linear algebra in ways that allow for better study of the groups in question. Over the last several decades, a number of results in the representations of solvable groups have been proven using so-called “large orbit” theorems. This book provides an extensive survey of the current state of the large-orbit theorems. The authors outline the proofs of the large orbit theorems to provide an overview of the topic, then demonstrate how these theorems can be used to prove new results about solvable groups.
The Representation Theory Of Finite Groups
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Author : W. Feit
language : en
Publisher: Elsevier
Release Date : 1982-05-01
The Representation Theory Of Finite Groups written by W. Feit and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-05-01 with Computers categories.
The Representation Theory of Finite Groups
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.
Modular Representations Of Finite Groups
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Author :
language : en
Publisher: Academic Press
Release Date : 1977-03-14
Modular Representations Of Finite Groups written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-03-14 with Mathematics categories.
Modular Representations of Finite Groups
Theory Of Group Representations And Applications
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Author : Asim Orhan Barut
language : en
Publisher: World Scientific
Release Date : 1986
Theory Of Group Representations And Applications written by Asim Orhan Barut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Representation Theory Of Finite Groups And Associative Algebras
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Author : Charles W. Curtis
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Representation Theory Of Finite Groups And Associative Algebras written by Charles W. Curtis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Provides an introduction to various aspects of the representation theory of finite groups. This book covers such topics as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations.
Representations Of Finite And Lie Groups
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Author : Charles Benedict Thomas
language : en
Publisher: Imperial College Press
Release Date : 2004
Representations Of Finite And Lie Groups written by Charles Benedict Thomas and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This book provides an introduction to representations of both finite and compact groups. The proofs of the basic results are given for the finite case, but are so phrased as to hold without change for compact topological groups with an invariant integral replacing the sum over the group elements as an averaging tool. Among the topics covered are the relation between representations and characters, the construction of irreducible representations, induced representations and Frobenius reciprocity. Special emphasis is given to exterior powers, with the symmetric group Sn as an illustrative example. The book concludes with a chapter comparing the representations of the finite group SL2(p) and the non-compact Lie group SL2(P).