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Author : Jean Pierre Serre
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.:/5 (86 download)
Download or read book Linear Representations of Finite Groups written by Jean Pierre Serre and published by . This book was released on 1996 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J.L. Alperin
Publisher : Springer Science & Business Media
ISBN 13 : 1461207991
Total Pages : 200 pages
Book Rating : 4.4/5 (612 download)
Download or read book Groups and Representations written by J.L. Alperin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise treatment of topics from group theory and representation theory for use in a one-term course. Focussing on the non-commutative side of the field, this advanced textbook emphasizes the general linear group as the most important group and example. Readers are expected to be familiar with groups, rings, and fields, and to have a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to introduce the reader to additional topics.
Author : E.B. Vinberg
Publisher : Birkhäuser
ISBN 13 : 3034892748
Total Pages : 151 pages
Book Rating : 4.0/5 (348 download)
Download or read book Linear Representations of Groups written by E.B. Vinberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.
Author : Brian Hall
Publisher : Springer
ISBN 13 : 3319134671
Total Pages : 452 pages
Book Rating : 4.3/5 (191 download)
Download or read book Lie Groups, Lie Algebras, and Representations written by Brian Hall and published by Springer. This book was released on 2015-05-11 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a self-contained construction of the representations of compact groups, independent of Lie-algebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finite-dimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended. — The Mathematical Gazette
Author : Pavel I. Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 0821853511
Total Pages : 240 pages
Book Rating : 4.8/5 (218 download)
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Dudley Ernest Littlewood
Publisher : American Mathematical Soc.
ISBN 13 : 0821840673
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Theory of Group Characters and Matrix Representations of Groups written by Dudley Ernest Littlewood and published by American Mathematical Soc.. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally written in 1940, this book remains a classical source on representations and characters of finite and compact groups. The book starts with necessary information about matrices, algebras, and groups. Then the author proceeds to representations of finite groups. Of particular interest in this part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynomials. The concluding chapters present the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The book, which can be read with minimal prerequisites (an undergraduate algebra course), allows the reader to get a good understanding of beautiful classical results about group representations.
Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
ISBN 13 : 082184377X
Total Pages : 594 pages
Book Rating : 4.8/5 (218 download)
Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author : Benjamin Steinberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461407761
Total Pages : 166 pages
Book Rating : 4.4/5 (614 download)
Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : A Barut
Publisher : World Scientific Publishing Company
ISBN 13 : 9813103876
Total Pages : 740 pages
Book Rating : 4.8/5 (131 download)
Download or read book Theory of Group Representations and Applications written by A Barut and published by World Scientific Publishing Company. This book was released on 1986-11-01 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this book originated from lectures given by authors over many years in Warsaw, Trieste, Schladming, Istanbul, Goteborg and Boulder. There is no other comparable book on group representations, neither in mathematical nor in physical literature and it is hoped that this book will prove to be useful in many areas of research. It is highly recommended as a textbook for an advanced course in mathematical physics on Lie algebras, Lie groups and their representations. Request Inspection Copy
Author : M.A. Naimark
Publisher : Springer
ISBN 13 : 9781461381440
Total Pages : 0 pages
Book Rating : 4.3/5 (814 download)
Download or read book Theory of Group Representations written by M.A. Naimark and published by Springer. This book was released on 2011-11-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author's Preface to the Russian Edition This book is written for advanced students, for predoctoral graduate stu dents, and for professional scientists-mathematicians, physicists, and chemists-who desire to study the foundations of the theory of finite dimensional representations of groups. We suppose that the reader is familiar with linear algebra, with elementary mathematical analysis, and with the theory of analytic functions. All else that is needed for reading this book is set down in the book where it is needed or is provided for by references to standard texts. The first two chapters are devoted to the algebraic aspects of the theory of representations and to representations of finite groups. Later chapters take up the principal facts about representations of topological groups, as well as the theory of Lie groups and Lie algebras and their representations. We have arranged our material to help the reader to master first the easier parts of the theory and later the more difficult. In the author's opinion, however, it is algebra that lies at the heart of the whole theory. To keep the size of the book within reasonable bounds, we have limited ourselves to finite-dimensional representations. The author intends to devote another volume to a more general theory, which includes infinite dimensional representations.
Author : Karin Erdmann
Publisher : Springer
ISBN 13 : 3319919989
Total Pages : 304 pages
Book Rating : 4.3/5 (199 download)
Download or read book Algebras and Representation Theory written by Karin Erdmann and published by Springer. This book was released on 2018-09-07 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Artin-Wedderburn theorem on the structure of semisimple algebras and the Krull-Schmidt theorem on indecomposable modules. The authors then go on to study representations of quivers in detail, leading to a complete proof of Gabriel's celebrated theorem characterizing the representation type of quivers in terms of Dynkin diagrams. Requiring only introductory courses on linear algebra and groups, rings and fields, this textbook is aimed at undergraduate students. With numerous examples illustrating abstract concepts, and including more than 200 exercises (with solutions to about a third of them), the book provides an example-driven introduction suitable for self-study and use alongside lecture courses.
Author : Ronald Shaw
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (831 download)
Download or read book Linear Algebra and Group Representations: Multilinear algebra and group representations written by Ronald Shaw and published by . This book was released on 1982 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jing-Song Huang
Publisher : World Scientific
ISBN 13 : 9789810237257
Total Pages : 206 pages
Book Rating : 4.2/5 (372 download)
Download or read book Lectures on Representation Theory written by Jing-Song Huang and published by World Scientific. This book was released on 1999 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Peter Webb
Publisher : Cambridge University Press
ISBN 13 : 1107162394
Total Pages : 339 pages
Book Rating : 4.1/5 (71 download)
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.
Author : Ronald Shaw
Publisher :
ISBN 13 :
Total Pages : 296 pages
Book Rating : 4.0/5 ( download)
Download or read book Linear Algebra and Group Representations: Linear algebra and introduction to group representations written by Ronald Shaw and published by . This book was released on 1982 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gordon James
Publisher : Cambridge University Press
ISBN 13 : 1139811053
Total Pages : 436 pages
Book Rating : 4.1/5 (398 download)
Download or read book Representations and Characters of Groups written by Gordon James and published by Cambridge University Press. This book was released on 2001-10-18 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern introduction to the representation theory of finite groups. Now in its second edition, the authors have revised the text and added much new material. The theory is developed in terms of modules, since this is appropriate for more advanced work, but considerable emphasis is placed upon constructing characters. Included here are the character tables of all groups of order less than 32, and all simple groups of order less than 1000. Applications covered include Burnside's paqb theorem, the use of character theory in studying subgroup structure and permutation groups, and how to use representation theory to investigate molecular vibration. Each chapter features a variety of exercises, with full solutions provided at the end of the book. This will be ideal as a course text in representation theory, and in view of the applications, will be of interest to chemists and physicists as well as mathematicians.
Author : R. Shaw
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (839 download)
Download or read book LINEAR ALGEBRA AND GROUP REPRESENTATIONS. written by R. Shaw and published by . This book was released on 1983 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
