Product Description
According to the author of this concise, high-level study, physicists often shy away from group theory, perhaps because they are unsure of which parts of the subject belong to the physicist and which belong to the mathematician. However, it is possible for physicists to understand and use many techniques which have a group theoretical basis without necessarily understanding all of group theory. This book is designed to familiarize physicists with those techniques. Specifically, the author aims to show how the well-known methods of angular momentum algebra can be extended to treat other Lie groups, with examples illustrating the application of the method. Chapter headings include such topics as isospin, the group SU3 and its application to elementary particles, the three-dimensional harmonic oscillator, algebras of operators which change the number of particles; permutations, bookkeeping and Young diagrams; the groups SU4, SU6 and SU12, an introduction to groups of higher rank, and more. Unabridged republication of the second edition of Lie Groups for Pedestrians, published by North-Holland Publishing Company, Amsterdam, 1966. Prefaces. Appendices. Bibliography. Subject Index.
... Read more

Customer Reviews (6)

Review of Lie groups for particle physics
This book is a nice, concise review of Lie algebras and groups as they are used in particle physics. The content is a bit dated, but the explanations of building the mathematical operators used in quantum mechanics are quite lucid. I think this would be an excellent companion to a more modern text on particle physics. This book is NOT Lie groups 101. Topics include the different flavors of spin, harmonic oscillators, multiplets of a few SU(n) groups, and tying everything back to Young diagrams.

The title is a bit misleading- if this is the "pedestrian" approach, I would hate to see what the author thinks is the more exotic route. The book jumps in right at basic angular momentum operators, so if it's been a while you might need to break out notes from a QM class. Important concepts are not defined, or are left as a vague mathematical mumbo-jumbo that doesn't at all hint at the underlying physical concept. Many times the author says "it clearly follows that..." or something similar, but I found it a nontrivial exercise to follow. Despite the fact that I had to go to other sources and push my pencil around a bit (probably my own shortcomings than anything in the book), I found this book easy enough to learn from.

best possible introduction for those with a background in QM
This is the best book I have come across to explain Lie groups/algebras to someone who has at least taken an introductory quantum mechanics course and is comfortable with the angular momentum operators-more particularly the raising/creation and lowering/annihilation operators. This is not for someone who has watched NOVA and wants to learn more. If you have a good background in group theory and quantum mechanics, or even a very basic understanding of them and you want to learn more about the fascinating word of Lie Algebras/groups, this book is for you.
As a companion to this book I would highly recommend Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore. This book gives an excellent exposition of the subject, going into more detail than Lie Groups for Pedestrians, but not so much detail that you need to have taken a course on group theory in order to digest the information. It also has very informative exercises at the end of the chapter, which in my opinion is a plus.
If you're looking for a quick and dirty introduction to string theory and that ilk, this is not your ticket. If you are looking to expand your horizons of QM theory and second quantization-which leads to wonderful results and 'toys' in not only particle physics, but also in spectroscopy of atoms and molecules-this is your book.

misleading title
I won't abound on what have already been said by one of the reviewers: "pedestrian" means "non mathematician, very well versed on Quantum Theory". But I liked to stress that this is not a book to learn Lie Group Theory from scratch. Far from that, I closed (and shelved) it at around page two.

I think I need "Lie Groups for Toddlers"
This book, by physicist Harry Lipkin, was intended as a quick introduction to Lie Groups to other physicists like himself working in the mid 1960's.At that time, many physicists had a sophisticated mathematical skill-set, but not one that included Lie Groups and Algebras, nor understood to the degree it is understood today how much it helps to think along those lines.Dr. Lipkin wanted to spread the knowledge of Lie Groups to physicists would would benefit from it.

As such, a "pedestrian" would be expected to be familiar with the then-current formulations of quantum theory, including the matrix and operator representations of quantum mechanics, as well as all the calculus necessary to work those theories.This is evident in chapter 1, where on page 2 section 1.1 is titled "Review of Angular Momentum Algebra", and whose first sentence asks us to consider the operators Jx, Jy, and Jz, which have the "well known" commutation rules [Jx,Jy]=iJz (etc).

Pedagogically, this is sound:start with something you know the reader is familiar with, then show by analogy how that applies to the new topic you are introducing, then expand the techniques into new areas, and then presumably turn it back towards the topic the reader knows and show how Lie Groups (in this case) make things easier.

However, it requires knowing the audience -- or, conversely, being the intended audience.I am not; from the benefit of knowing where physics has gone in the intervening 42 years, I know Lie Groups are important, and I know that my understanding of physics is weak, and I was hoping knowing about Lie Groups would help my understanding of physics.Ultimately, this book lost me before page 5.

I suspect this book no longer has an audience.The importance of Lie Groups in physics is now well-recognized and is taught to physicists-in-training.The folks who would understand this book no longer need it.Historically, it might have been important, but it no longer is.

Top ten classical but nowadays incomplete review of group theory in Physics
The book of Lipkin has become a classical reference in group theoretical methods in physics, and is one of the most valuable reviews at the time of the establishment of the Gell-Mann-Ne'emanoctet model. Divided into seven chapters and various later written appendixes, this work was originally thought as a comprehensive introduction to the unitary symmetry. This has been achieved in an impressive way, as shows the careful development of the topics and successive refinements. The su(3) symmetry is deduced naturally starting from the annihilation-creation operator formalism employed for the nucleon, and introducing the needed tools step by step. The (1966) more relevant groups SU(3), SU(4), SU(6) and SU(12) groups are analyzed in some detail, as well as some low rank symplectic groups and various subgroups intervening in the state labeling problem, such as the Wigner supermultiplet model. The author makes a self-contained presentation of the combinatorial technique of Young diagrams, which is inspired in the milestone work of M. Hammermesh, but presented here with astonishing simplicity to be applied by the reader without requiring a deep theoretical background.
A quite interesting section is devoted to the experimental predictions obtained from the octet model, like the classical example of the negative hyperon, discovered by Barnes et al. following the theoretical model. In all, this book shows the situation of the global internal symmetries in the 60s.
There is however one surprising fact about the book. In spite of the title, the concept of Lie group is nowhere defined adequately through the book. Although it is commonly understood that the group is meant when working with the corresponding Lie algebra, this can mislead some readers. Also the (informal) definition of Lie algebra given in equation (1.15) on page ten is false, or at least incomplete. A set of operators with some bracket (either of bosonic or fermionic type) defines a Lie algebra only if it is closed with respect to this brackets and additionally satisfies the Jacobi identity. None of this is found in the definition given in the book.To "satisfy commutation relations similar to those of angular momentum operators" is definitively not sufficient for higher rank algebras. I agree that this minor detail is irrelevant for the rest of the book, because the used operators obviously define a Lie algebra, but this can also lead to confusion, since apparently any arbitrary collection of operators would have the same property.

Although this book has aged quite well and remains an important reference, it is no more adequate for those who want an actualized overview of the classification of particles. There are obvious reasons for this, as the non-covered topics correspond to concepts or models that were developed later than the publication of the book. One example is the attribute color (around 1973), introduced to explain some remaining difficulties. This absence obviously extends to QCD (Quantum Chromodynamics). Also the unified theories and the modelSU(5) of Georgi-Glashow(1974) are not covered, as well as the symmetry broken down from this group to the reductive group SU(3) x SU(2) x U(1), or the resulting proton decay. Such important absences, easily detected by the expert, are not immediate for the beginner. However, there is no doubt that this book is an excellent introduction to the specific problems of group theory applied to particle physics. In any case, in order to have a larger comprehension of the topic, the text must be completed with the reading of more modern or detailed monographs. Good complements to the book of Lipkin containing later developments and theories would be, for example, the work of Ne'eman [Symétries jauge et variétés de groupe, PUM, Montréal, 1979], the book of Georgi [Lie algebras in particle physics, Perseus Books, Reading, 1982] or the encyclopedic work of Cornwell [Group theory in physics, Academic Press, San Diego, 1984, volume 2]. ... Read more

Product Description
Perhaps the first truly famous book devoted primarily to finite groups was Burnside's book. From the time of its second edition in 1911 until the appearance of Hall's book, there were few books of similar stature. Hall's book is still considered to be a classic source for fundamental results on the representation theory for finite groups, the Burnside problem, extensions and cohomology of groups, $p$-groups and much more. For the student who has already had an introduction to group theory, there is much treasure to be found in Hall's Theory of Groups. From the Preface to the Second Edition (1976): ``The present volume is intended to serve a dual purpose. The first ten chapters are meant to be the basis for a course in group theory, and exercises have been included at the end of each of these chapters. The last ten chapters are meant to be useful as optional material in a course or as reference material. When used as a text, the book is intended for students who have had an introductory course in modern algebra comparable to a course taught from Birkhoff and Mac Lane's A Survey of Modern Algebra. I have tried to make this book as self-contained as possible, but where background material is needed references have been given, chiefly to Birkhoff and Mac Lane.'' ... Read more

Customer Reviews (1)

Its just that good
If you are looking for an introductory book on group theory, I suggest Herstein or Dummit & Foote, but for an intermediate to advanced group theory student, you can't do much better. Marshall Hall is an excellentmathematician who writes an excellent book, full of examples and expositorythat makes for the book being a good read, and an astounding reference. Asfor learning the material, even now I go back to sections of book I didn'tcover in the class I used it, to learn material for classes I am currentlyin. It covers the basics of group theory (in fact, he gives severalversions of the definition of a group), free groups, compostion series,solvable groups, nilpotent groups, p-groups, cohomology, and does andincredible introduction into representation and character theory. This bookdoes the best a math book can do, it teaches well. ... Read more

Product Description

Product Description
In this volume the author gives an introduction to the theory of group representations and their applications in image science. The main feature of the presentation is a systematic treatment of the invariance principle in image processing and pattern recognition with the help of group theoretical methods. The invariance properties of a problem often largely define the solution to the problem. Invariance principles are well known in theoretical physics but their use in image processing is only a few years old. The reader will find that group theory provides a unifying framework for many problems in image science. The volume is based on graduate-level lectures given by the author, and the book is intended for students and researchers interested in theoretical aspects of computer vision. ... Read more

Product Description
This volume contains selected papers from the international conference Tits Buildings and the Model Theory of Groups, held in WÜrzburg in 2000. The first part provides a general introduction to many aspects of buildings and their geometries, based on short lecture courses given at the conference. The rest of the book comprises survey and research articles on model theoretic results and techniques. Amalgamation constructions a la Hrushovski are explained and classified, as they are important techniques both in model theory and geometry. The articles demonstrate the close connection between geometry, group theory, and model theory. ... Read more

Product Description

From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews

Customer Reviews (1)

Simply Awesome
I don't think I could come up with enough superlatives to describe just how good this text really is.Both authors have done an excellent job describing as well as motivating the subject and have subsequently turned me into an avid fan of the theory of finite groups.What I find disappointing is my assumption that the available pool of readers is more like a shallow puddle.This can easily be seen from the fact that, as thriving of a subject finite groups may be, it does not appear in the course catalog of most academic institutions.It would be nice to see this book adopted as a seniors honor course for undergraduates or as an advanced algebra course for graduate students looking to specialize in matters algebraic. Now, off my soap box.Without a doubt this text will become another classic in the field of finite groups, akin to Gorenstein's.So who can read this text?Well, as un-original as it is, the mathematically mature and, more importantly, anyone who has taken an Algebra course that covered the standard basics of group theory.To be exact, if you learned Algebra using Hungerford's text, then you should be adequately prepared for this book.Of course this assumes you have seen and understand the how's/why's of the Sylow theorems, the structure and purpose of Abelian groups, the role Normality plays and, in my opinion, you should have a firm grasp of the role/structure/purpose of the various types of morphisms (homomorphism, epimorphism, monomorphism, and isomorphism)and how and why they are so important in group theory.The only drawback to this book is that the exercises seemingly disappear after page 223 in the chapter dealing with groups acting on groups.I know the material becomes more dense, more difficult and more abstract but, I would have assumed that the authors could have provided the reader with exercises post chapter 8 (even if the exercise was finishing a proof).Aside from that, I would recommend this text to everyone and anyone.In particular, if you are not a math wiz and just plain interested in learning about finite groups, then I would suggest that you pick up this text.Good luck and happy proving! ... Read more

Product Description

Product Description
First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation theory, including a masterly treatment of topics such as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations. These and many other subjects are treated extremely thoroughly, starting with basic definitions and results and proceeding to many important and crucial developments. Numerous examples and exercises help the reader of this unsurpassed book to master this important area of mathematics. ... Read more

Product Description
The Theory of Groups and Quantum Mechanics, Good Condition, 1931. ... Read more

Product Description
Since its origin in the early 20th century, combinatorial group theory has been primarily concerned with algorithms for solving particular problems on groups given by generators and relations: word problems, conjugacy problems, isomorphism problems, etc. Recent years have seen the focus ofalgorithmic group theory shift from the decidability/undecidability type of result to the complexity of algorithms. Papers in this volume reflect that paradigm shift. Articles are based on the AMS/ASL Joint Special Session, Interactions Between Logic, Group Theory and Computer Science. The volume issuitable for graduate students and research mathematicians interested in computational problems of group theory. ... Read more

Product Description
The representation theory of the symmetric groups is a classical topic that, since the pioneering work of Frobenius, Schur and Young, has grown into a huge body of theory, with many important connections to other areas of mathematics and physics. This self-contained book provides a detailed introduction to the subject, covering classical topics such as the Littlewood-Richardson rule and the Schur-Weyl duality. Importantly the authors also present many recent advances in the area, including Lassalle's character formulas, the theory of partition algebras, and an exhaustive exposition of the approach developed by A. M. Vershik and A. Okounkov. A wealth of examples and exercises makes this an ideal textbook for graduate students. It will also serve as a useful reference for more experienced researchers across a range of areas, including algebra, computer science, statistical mechanics and theoretical physics. ... Read more

Product Description

Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis.

Key to this unique exposition is the large amount of background material presented so the book is accessible to a reader with relatively modest mathematical background. Historical information, examples, exercises are all woven into the text.

Lie Groups: An Approach through Invariants and Representations will engage a broad audience, including advanced undergraduates, graduates, mathematicians in a variety of areas from pure algebra to functional analysis and mathematical physics.

Customer Reviews (1)

Beautiful book
This is a beautiful book. From what I have read so far, it is very clearly written (undoubtedly the product of years of rewritings and revisions), connecting topics that are very connected but normally never included in one book on Lie groups (including symmetric functions, tableaux and many other topics from algebraic combinatorics). I plan to write a more detailed review once I have finished reading it, but at 600 pages (of densely packed but very well organized information) and less than US$50.00, it is very highly recommended as a textbook and as a reference.

PS If this book were published by Kluwer, they would probably be charging US$500.00 ... Read more

Customer Reviews (3)

You can't put this one down!
The greatest book ever! Robert J. Zimmer captures the greatest math ever in this book! I read a book resently called To Kill A Mockingbird and it doesnt compare in any way to this perfect book.This book is a must read by all.You cant put this one down!Read it!Its great!

Two Thumbs Up
In all my years of studying mathematics, I have never encountered a more comprehensive text on semisimple groups and ergodic theory.I highly recomend this book to everyone from the amateur math lover to the greatest mathematician.Two thumbs up.

GREAT READING FOR THE WHOLE FAMILY
This book is one of the best I've ever read on semisimple groups.It evenrivals G. A. Margulis's "Discrete Subgroups of Semisimple LieGroups" as the best book I have ever read on semisimple groups. Furthermore, Zimmer's insight into Ergodic Theory is truely revolutionary. The entire book is great for all purposes, especially bedtime reading. Also, make sure to read it to to the kids; they'll love it.So, if youwant the ver-i-tas about semisimple lie groups, ingeneous insights intoergodic theory, and great reading for the whole family - especially thekids, then make sure to read one of the great classics of the twentiethcentury: "Ergodic Theory and Semisimple Groups" by Robert J.Zimmer! ... Read more

Product Description
This volume presents a fully self-contained introduction to the modular representation theory of the Iwahori-Hecke algebras of the symmetric groups and of the $q$-Schur algebras. The study of these algebras was pioneered by Dipper and James in a series of landmark papers. The primary goal of the book is to classify the blocks and the simple modules of both algebras. The final chapter contains a survey of recent advances and open problems. The main results are proved by showing that the Iwahori-Hecke algebras and $q$-Schur algebras are cellular algebras (in the sense of Graham and Lehrer). This is proved by exhibiting natural bases of both algebras which are indexed by pairs of standard and semistandard tableaux respectively. Using the machinery of cellular algebras, which is developed in Chapter 2, this results in a clean and elegant classification of the irreducible representations of both algebras. The block theory is approached by first proving an analogue of the Jantzen sum formula for the $q$-Schur algebras. This book is the first of its kind covering the topic. It offers a substantially simplified treatment of the original proofs. The book is a solid reference source for experts. It will also serve as a good introduction to students and beginning researchers since each chapter contains exercises and there is an appendix containing a quick development of the representation theory of algebras. A second appendix gives tables of decomposition numbers. ... Read more

Product Description
Research in group theory have resulted in a large number of books written for postgraduates in the subject, but a good introductory text is difficult to find. This book fills the gap, providing a clear and comprehensive introduction to the theory of groups and covering all topics likely to be encountered in undergraduate courses. Introductory chapters explain the concepts of group, subgroup and normal subgroup, and quotient group. The homomorphism and isomorphism theorems are explained, along with an introduction to G-sets. Subsequent chapters deal with finite abelian groups, the Jordan-Holder theorem, soluble groups, p-groups, and group extensions. The numerous worked examples and exercises in this excellent and self-contained introduction will also encourage undergraduates (and first year graduates) to further study. ... Read more

Customer Reviews (2)

nice
this is a concise and fairly comprehensive book on finite groups.

it is very, very nice.in about 200 pages, it gives you all of the basics. a bright high school student can read it.

books like these are so much better than annoying books like Artin, or Lang which are like 700 pages and are basically a brain dump of the author onto the student.

if you want to learn group theory by yourself and have a patience, read this book, then the book by James and Liebeck.then to learn Lie algebras/groups, use a book like Erdmann or Kirillov or this very short new book by Yvette Kosmann-Schwarzbach.for lots of examples look at Fulton & Harris.

A Gentle but Inclusive Introduction
The book covers all the elements of group theory,
with a great deal of care.Each concept introduced
is supported with at least some examples, difficult
concepts with many.The book is rigorous without
being pedantic.The last chapter, which I could not
resist skipping to, contains a survey of the description
of finite groups with some historical notes and indications
of where the reader might go next.I am looking for
other books by the same author.It is obfious from
this book that the author is an excellent teacher. ... Read more

Product Description
In most mathematics textbooks, the most exciting part of mathematics--the process of invention and discovery--is completely hidden from the reader. The aim of Groups and Symmetry is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: Its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you.

Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with nonscience students who want to fulfill a science requirement. ... Read more

Customer Reviews (2)

the best math textbook I've ever had
This book was the foundational textbook for a 100-level class in symmetry at my university. I recommend it highly to anyone who wants to get a better feel for what mathematicians actually do and think about and work with. Folks who never got into the higher math classes often have a different idea of what mathematics is all about than mathematicians. At the level of introductory algebra and geometry and even some calculus, math education often seems to be mainly about memorizing formulas and recognizing in which situations to apply them. That's an important thing to learn, but it is not useful for imparting an idea and a feel of the field of mathematics as a whole. Farmer's book brings home the understanding that mathematics is, at its heart, about patterns and that mathematics is not so much about memorization and application as it is about discovery.

The level of mathematical understanding required to get something useful out of this book is low. I believe the professor required beginning algebra as the prerequisite. If you can count to six, recognize the difference between a square and a pentagon, and understand that variables like n, m, or x can be used as substitutes for numbers then you probably have enough mathematical sophistication to work your way through this book and gain insights into the beauty of higher math.

An excellent primer on abstract algebra
Groups are the first structures encountered in abstract algebra and form the foundation for most of the others. Fortunately, they are also the easiest to physically represent, so in some sense they are the most concrete. In this book, groups are introduced as the motions and structures of geometric figures, so the presentation is largely by diagram rather than formula. Very little previous knowledge of mathematics is required and after reading the book, you will have a solid understanding of what a group is.
The first topic is the moving of a complete figure to a different location of the plane defined by a grid of points. By keeping the figure rigid and fixed in orientation, a set of legal moves is defined. After that, some of the rules are relaxed and that allows for additional moves to be added. Exercises and problems are put forward here and throughout the book, and with the accent on figures, often give the appearance of a game.
The next steps are then to allow for all possible rotations, translations and reflections of the objects, using these to explain the structure of a group. This is an effective way to introduce group theory, and is how I will do it if I teach abstract algebra again. Permutation and plane tiling symmetry groups are then introduced and examined, and their relationship to the previous groups discussed, which introduces the concept of isomorphism.
Basic group theory is something that everyone can understand, as humans have a natural affinity for patterns and recognizing them despite "trivial" alterations. This book is an excellent primer on group theory and I strongly recommend it to anyone either learning or teaching abstract algebra.

Published in Journal of Recreational Mathematics, reprinted with permission. ... Read more

Product Description
This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Application methods to physics are emphasized. New materials drawn from the teaching and research experience of the author are included. This book can be used by graduate students and young researchers in physics, especially theoretical physics. It is also suitable for some graduate students in theoretical chemistry. ... Read more

Product Description
Collection of papers on gender-oriented psychodynamic group psychotherapy, with a feminist-theory emphasis. For therapists. 24 contributors, 23 U.S. DNLM: Psychotherapy, Group. ... Read more