Group Matrices Group Determinants And Representation Theory

Author : Kenneth W. Johnson
Publisher : Springer Nature
Page : 384 pages
File Size : 53,6 Mb
Release : 2019-11-08
Category : Mathematics
ISBN : 9783030283001

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Group Matrices, Group Determinants and Representation Theory by Kenneth W. Johnson Pdf

This book sets out an account of the tools which Frobenius used to discover representation theory for nonabelian groups and describes its modern applications. It provides a new viewpoint from which one can examine various aspects of representation theory and areas of application, such as probability theory and harmonic analysis. For example, the focal objects of this book, group matrices, can be thought of as a generalization of the circulant matrices which are behind many important algorithms in information science. The book is designed to appeal to several audiences, primarily mathematicians working either in group representation theory or in areas of mathematics where representation theory is involved. Parts of it may be used to introduce undergraduates to representation theory by studying the appealing pattern structure of group matrices. It is also intended to attract readers who are curious about ideas close to the heart of group representation theory, which do not usually appear in modern accounts, but which offer new perspectives.

Author : Dudley Ernest Littlewood
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 44,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821840672

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The Theory of Group Characters and Matrix Representations of Groups by Dudley Ernest Littlewood Pdf

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 : Martin Burrow
Publisher : Academic Press
Page : 196 pages
File Size : 48,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483258218

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Representation Theory of Finite Groups by Martin Burrow Pdf

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.

Author : Charles W. Curtis
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 44,6 Mb
Release : 2024-06-23
Category : Mathematics
ISBN : 0821896725

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Pioneers of Representation Theory by Charles W. Curtis Pdf

The year 1897 was marked by two important mathematical events: the publication of the first paper on representations of finite groups by Ferdinand Georg Frobenius (1849-1917) and the appearance of the first treatise in English on the theory of finite groups by William Burnside (1852-1927). Burnside soon developed his own approach to representations of finite groups. In the next few years, working independently, Frobenius and Burnside explored the new subject and its applications to finite group theory. They were soon joined in this enterprise by Issai Schur (1875-1941) and some years later, by Richard Brauer (1901-1977). These mathematicians' pioneering research is the subject of this book. It presents an account of the early history of representation theory through an analysis of the published work of the principals and others with whom the principals' work was interwoven. Also included are biographical sketches and enough mathematics to enable readers to follow the development of the subject. An introductory chapter contains some of the results involving characters of finite abelian groups by Lagrange, Gauss, and Dirichlet, which were part of the mathematical tradition from which Frobenius drew his inspiration. This book presents the early history of an active branch of mathematics. It includes enough detail to enable readers to learn the mathematics along with the history. The volume would be a suitable text for a course on representations of finite groups, particularly one emphasizing an historical point of view. Co-published with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.

Author : Gilbert de Beauregard Robinson
Publisher : Edinburgh : University Press
Page : 218 pages
File Size : 46,6 Mb
Release : 1961
Category : Group theory
ISBN : UCAL:B4249445

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Representation Theory of the Symmetric Group by Gilbert de Beauregard Robinson Pdf

Author : Larry L. Dornhoff
Publisher : Unknown
Page : 280 pages
File Size : 50,9 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015014354446

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Group Representation Theory: Ordinary representation theory by Larry L. Dornhoff Pdf

Author : Victor E Hill
Publisher : CRC Press
Page : 239 pages
File Size : 54,6 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351443814

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Groups and Characters by Victor E Hill Pdf

Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. This book offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, it emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The text includes sections that provide the mathematical basis for some of the applications of group theory. It also offers numerous exercises, some stressing computation of concrete examples, others stressing development of the theory.

Author : Meinolf Geck
Publisher : EPFL Press
Page : 472 pages
File Size : 54,5 Mb
Release : 2007-05-07
Category : Mathematics
ISBN : 0849392438

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Group Representation Theory by Meinolf Geck Pdf

After the pioneering work of Brauer in the middle of the 20th century in the area of the representation theory of groups, many entirely new developments have taken place and the field has grown into a very large field of study. This progress, and the remaining open problems (e.g., the conjectures of Alterin, Dade, Broué, James, etc.) have ensured that group representation theory remains a lively area of research. In this book, the leading researchers in the field contribute a chapter in their field of specialty, namely: Broué (Finite reductive groups and spetses); Carlson (Cohomology and representations of finite groups); Geck (Representations of Hecke algebras); Seitz (Topics in algebraic groups); Kessar and Linckelmann (Fusion systems and blocks); Serre (On finite subgroups of Lie groups); Thévenaz (The classification of endo-permutaion modules); and Webb (Representations and cohomology of categories).

Author : John Atwell Moody
Publisher : World Scientific
Page : 184 pages
File Size : 48,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9810221053

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Groups for Undergraduates by John Atwell Moody Pdf

In these lecture notes the student learns basic theorems of the subject (due to Sylow, Burnside, Schur and Frobenius). More importantly, the student learns to use the theorems in various combinations, to discover for himself the groups of reasonably small order. In examples, presentations of the groups of order 1?31 and 33?42 are constructed.Once the groups are presented abstractly, the problem is not done: one needs to know how each abstract group may arise as a group of permutations or matrices. Theorems and techniques of representation theory are given which can do this for any group the student may have constructed in the earlier chapters ? and the student ends up building the actual representations (not only the characters). In a series of examples, which the student may carry further, all the matrix representations are constructed for the groups of order less than 13.For students who are already familiar with homomorphisms, cosets, Lagrange's theorem, and finite abelian groups, the text may be used alone. For any group theory course, at least one text such as this one, containing lots of examples, is strongly recommended.The book is written in a lucid, straightforward style. The subject matter is presented from a student's perspective and constantly demands the student's involvement. Both these strategies are highly appropriate for a book of lecture notes and guarantee the student's understanding of the mathematical concepts.

Author : Michler,Ringel
Publisher : Birkhäuser
Page : 526 pages
File Size : 52,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886581

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Representation Theory of Finite Groups and Finite-Dimensional Algebras by Michler,Ringel Pdf

From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.

Author : J.L. Alperin,Rowen B. Bell
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 42,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461207993

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Groups and Representations by J.L. Alperin,Rowen B. Bell Pdf

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 : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 50,8 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455927

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Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Author : T. Tom Dieck
Publisher : Springer
Page : 317 pages
File Size : 47,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540385172

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Transformation Groups and Representation Theory by T. Tom Dieck Pdf

Author : R.L. Lipsman
Publisher : Springer
Page : 176 pages
File Size : 51,6 Mb
Release : 2006-08-01
Category : Mathematics
ISBN : 9783540384021

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Group Representations by R.L. Lipsman Pdf

Author : Francis D. Murnaghan
Publisher : Unknown
Page : 392 pages
File Size : 47,5 Mb
Release : 2005
Category : Mathematics
ISBN : CORNELL:31924102012170

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The Theory of Group Representations by Francis D. Murnaghan Pdf

Francis D. Murnaghan, a distinguished contributor in the sphere of applied mathematics, created this comprehensive introduction to the theory of group representations. Murnaghan's first-rate account of the field pioneered and developed chiefly by Frobenius, Weyl, and Schur devotes particular attention to the groups—mainly the symmetric group and the rotation group—of fundamental significance for quantum mechanics (especially nuclear physics). Because groups of matrices are the usual group representations, this work is also a valuable contribution to the literature on matrices. The author places particular emphasis on such topics as the theory of group integration, the theory of two-valued or spin representations, the representations of the symmetric group and the analysis of their direct products, the crystallographic groups, and the Lorentz group and the concept of semivectors. Other sections cover groups and matrices, reducibility, group characters, the alternating group, linear groups, and the orthogonal group. This authoritative exposition is of specific interest to teachers and graduate-level students of applied mathematics, physics, and higher algebra.