Groups and Symmetries: From Finite Groups to Lie Groups

Paperback | October 28, 2009

byYvette Kosmann-SchwarzbachTranslated byStephanie Frank Singer

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The theory of group representations is a fundamental subject at the intersection of algebra, geometry and analysis, with innumerable applications in other domains of pure mathematics and in the physical sciences: chemistry, molecular biology and physics, in particular crystallography, classical and quantum mechanics and quantum field theory.Topics include:- brisk review of the basic definitions and fundamental results of group theory, illustrated with examples;- representation theory of finite groups (Schur's Lemma and characters) and, using Haar measure, its generalization to compact groups;- Lie algebras and linear Lie groups;- detailed study of the group of rotations, the special unitary group in dimension 2 and their representations;- spherical harmonics;- representations of the special unitary group in dimension 3 (roots and weights) with quark theory as a consequence of the mathematical properties of the symmetry group.This book is an introduction to both the theory of group representations and its applications in quantum mechanics. Unlike many other texts, it deals with finite groups, compact groups, linear Lie groups and their Lie algebras, concisely presented in one volume. With only linear algebra and calculus as prerequisites, it is accessible to advanced undergraduates in mathematics and physics, and will still be of interest to beginning graduate students. Exercises for each chapter and a collection of problems with complete solutions make this an ideal text for the classroom or for independent study.

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From the Publisher

The theory of group representations is a fundamental subject at the intersection of algebra, geometry and analysis, with innumerable applications in other domains of pure mathematics and in the physical sciences: chemistry, molecular biology and physics, in particular crystallography, classical and quantum mechanics and quantum field t...

From the Jacket

Unlike many other texts, this book deals with the theory of representations of finite groups, compact groups, linear Lie groups and their Lie algebras, concisely and in one volume.Key Topics:. Brisk review of the basic definitions of group theory, with examples. Representation theory of finite groups: character theory. Representations ...

A former student of the École Normale Supérieure, Yvette Kosmann-Schwarzbach holds a Doctorat d'État in mathematics as well as a degree in physics from the University of Paris. She has been a professor of mathematics at the University of Lille, at Brooklyn College of the City University of New York, and most recently at the École Polyt...

other books by Yvette Kosmann-Schwarzbach

Format:PaperbackDimensions:212 pages, 9.25 × 6.1 × 0 inPublished:October 28, 2009Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387788654

ISBN - 13:9780387788654

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Table of Contents

Introduction.- Acknowledgments.- General Facts about Groups.- Representations of Finite Groups.- Representations of Compact Groups.- Lie Groups and Lie Algebras.- Lie groups SU(2) and SO(3).- Representations of SU(2) and SO(3).- Spherical Harmonics.- Representations of SU(3) and Quarks.- Problems and Solutions.- Bibliography.- Index.

Editorial Reviews

From the reviews:"Groups and Symmetries is a short, concise book . that provides an introduction to the subject of Lie Groups, Lie Algebras, their representations, and their uses in theoretical particle physics. . Anyone interested in understanding the connection between quarks and representation theory is an expeditious fashion should read this book. . at the end of each chapter, Groups and Symmetries has a helpful reference section that provides readers with historical comments and additional references to the topics covered." (Thomas R. Hagedorn, The Mathematical Association of America, April, 2010)"This book by Kosmann-Schwarzbach (École Polytechnique, France) also starts with the basics but rapidly moves on to enrich group theory with notions from topology, analysis, and (multi) linear algebra. Surely one finds many monographs on Lie groups for students on the way to specializing. . Summing Up: Recommended. Upper-division undergraduates, graduate students, and professionals." (D. V. Feldman, Choice, Vol. 47 (11), July, 2010)"This book gives a gentle introduction to the theory of group representations and its applications in quantum mechanics. . This book is well written and is well suited for a course aimed at advanced undergraduates and early graduate students." (Aloysius Helminck, Mathematical Reviews, Issue 2011 g)"The author gives a very clear and comprehensible introduction to the representation theory of groups focussing in particular on Lie groups. . A series of nine problems and solutions completes this well thought-out and well organized book, which can be recommended already to advanced undergraduates." (G. Kowol, Monatshefte für Mathematik, Vol. 164 (2), October, 2011)