Group Matrices, Group Determinants and Representation Theory
Group Matrices, Group Determinants and Representation Theory

Author: Kenneth W. Johnson

Publisher: Springer Nature

Published: 2019-11-08

Total Pages: 400

ISBN-13: 3030283003

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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.

Representation Theory of Finite Groups
Representation Theory of Finite Groups

Author: Benjamin Steinberg

Publisher: Springer Science & Business Media

Published: 2011-10-23

Total Pages: 166

ISBN-13: 1461407761

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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.

Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer
Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer

Author: Charles W. Curtis

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 308

ISBN-13: 0821826778

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The AMS History of Mathematics series is one of the most popular items for bookstore sales. These books feature colorful, attractive covers that are perfect for face out displays. The topics will appeal to a broad audience in the mathematical and scientific communities.

Representation Theory of Finite Groups
Representation Theory of Finite Groups

Author: Martin Burrow

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 196

ISBN-13: 1483258211

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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.

Introduction to Representation Theory
Introduction to Representation Theory

Author: Pavel I. Etingof

Publisher: American Mathematical Soc.

Published: 2011

Total Pages: 240

ISBN-13: 0821853511

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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 of Finite Groups and Finite-Dimensional Algebras
Representation Theory of Finite Groups and Finite-Dimensional Algebras

Author: Michler

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 526

ISBN-13: 3034886586

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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.

Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry
Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry

Author: Sergey Novikov

Publisher: American Mathematical Soc.

Published: 2021-04-12

Total Pages: 480

ISBN-13: 1470455927

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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.

Mathematical Conversations
Mathematical Conversations

Author: Robin Wilson

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 486

ISBN-13: 1461301955

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Approximately fifty articles that were published in The Mathematical Intelligencer during its first eighteen years. The selection demonstrates the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. Each article is introduced by the editors. "...The Mathematical Intelligencer publishes stylish, well-illustrated articles, rich in ideas and usually short on proofs. ...Many, but not all articles fall within the reach of the advanced undergraduate mathematics major. ... This book makes a nice addition to any undergraduate mathematics collection that does not already sport back issues of The Mathematical Intelligencer." D.V. Feldman, University of New Hamphire, CHOICE Reviews, June 2001.

The Symmetric Group in Quantum Chemistry
The Symmetric Group in Quantum Chemistry

Author: R. Pauncz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 260

ISBN-13: 1351094122

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This is the first book to provide comprehensive treatment of the use of the symmetric group in quantum chemical structures of atoms, molecules, and solids. It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin eigenfunctions. The heart of the book is in the chapter dealing with spin-free quantum chemistry showing the great interpretation value of this method. The last three chapters include the unitary group approach, the symmetric group approach, and the spin-coupled valence bond method. An extensive bibliography concludes the book.

Group Theory
Group Theory

Author: R. Mirman

Publisher: World Scientific

Published: 1995

Total Pages: 494

ISBN-13: 9789810233655

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A thorough introduction to group theory, this (highly problem-oriented) book goes deeply into the subject to provide a fuller understanding than available anywhere else. The book aims at, not only teaching the material, but also helping to develop the skills needed by a researcher and teacher, possession of which will be highly advantageous in these very competitive times, particularly for those at the early, insecure, stages of their careers. And it is organized and written to serve as a reference to provide a quick introduction giving the essence and vocabulary useful for those who need only some slight knowledge, those just learning, as well as researchers, and especially for the latter it provides a grasp, and often material and perspective, not otherwise available.