Representation Theory
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Lectures On Representation Theory
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Author : Jing-Song Huang
language : en
Publisher: World Scientific
Release Date : 1999
Lectures On Representation Theory written by Jing-Song Huang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is an expanded version of the lectures given at the Nankai Mathematical Summer School in 1997. It provides an introduction to Lie groups, Lie algebras and their representations as well as introduces some directions of current research for graduate students who have little specialized knowledge in representation theory. It only assumes that the reader has a good knowledge of linear algebra and some basic knowledge of abstract algebra.Parts I-III of the book cover the relatively elementary material of representation theory of finite groups, simple Lie algebras and compact Lie groups. These theories are natural continuation of linear algebra. The last chapter of Part III includes some recent results on extension of Weyl's construction to exceptional groups. Part IV covers some advanced material on infinite-dimensional representations of non-compact groups such as the orbit method, minimal representations and dual pair correspondences, which introduces some directions of the current research in representation theory.
A Tour Of Representation Theory
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Author : Martin Lorenz
language : en
Publisher: American Mathematical Soc.
Release Date : 2018
A Tour Of Representation Theory written by Martin Lorenz 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 2018 with Categories (Mathematics) categories.
Representation theory investigates the different ways in which a given algebraic object--such as a group or a Lie algebra--can act on a vector space. Besides being a subject of great intrinsic beauty, the theory enjoys the additional benefit of having applications in myriad contexts outside pure mathematics, including quantum field theory and the study of molecules in chemistry. Adopting a panoramic viewpoint, this book offers an introduction to four different flavors of representation theory: representations of algebras, groups, Lie algebras, and Hopf algebras. A separate part of the book is devoted to each of these areas and they are all treated in sufficient depth to enable and hopefully entice the reader to pursue research in representation theory. The book is intended as a textbook for a course on representation theory, which could immediately follow the standard graduate abstract algebra course, and for subsequent more advanced reading courses. Therefore, more than 350 exercises at various levels of difficulty are included. The broad range of topics covered will also make the text a valuable reference for researchers in algebra and related areas and a source for graduate and postgraduate students wishing to learn more about representation theory by self-study.
Introduction To Representation Theory
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Author : Pavel I. Etingof
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Introduction To Representation Theory written by Pavel I. Etingof 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 2011 with Mathematics categories.
Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Representation Theory
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Author : William Fulton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Representation Theory written by William Fulton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The primary goal of these lectures is to introduce a beginner to the finite dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.
Representation Theory Of Finite Groups
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Author : Martin Burrow
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Representation Theory Of Finite Groups written by Martin Burrow and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.
An Introduction To The Representation Theory Of Groups
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Author : Emmanuel Kowalski
language : en
Publisher: American Mathematical Society
Release Date : 2014-08-28
An Introduction To The Representation Theory Of Groups written by Emmanuel Kowalski and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-28 with Mathematics categories.
Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.
Representation Theory
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Author : Alexander Zimmermann
language : en
Publisher: Springer
Release Date : 2014-08-15
Representation Theory written by Alexander Zimmermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with Mathematics categories.
Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Representation Theory Of Finite Groups And Associative Algebras
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Author : Charles W. Curtis
language : en
Publisher: American Mathematical Soc.
Release Date : 1966
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 1966 with Mathematics categories.
Representation Theory Of Finite Groups
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Author : Benjamin Steinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-23
Representation Theory Of Finite Groups written by Benjamin Steinberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-23 with Mathematics categories.
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
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.