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Introduction to Lie Algebras and Representation Theory (Graduate Texts in Mathematics) (v. 9)

3.9 out of 5 stars 9 customer reviews
ISBN-13: 000-0387900535
ISBN-10: 0387900535
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Editorial Reviews

Review

J.E. Humphreys

Introduction to Lie Algebras and Representation Theory

"An excellent introduction to the subject, ideal for a one semester graduate course."THE AMERICAN MATHEMATICAL MONTHLY

"Exceptionally well written and ideally suited either for independent reading or as a text for an introduction to Lie algebras and their representations."MATHEMATICAL REVIEWS

J.E. Humphreys

Introduction to Lie Algebras and Representation Theory

"An excellent introduction to the subject, ideal for a one semester graduate course."???THE AMERICAN MATHEMATICAL MONTHLY

"Exceptionally well written and ideally suited either for independent reading or as a text for an introduction to Lie algebras and their representations."???MATHEMATICAL REVIEWS

J.E. Humphreys

Introduction to Lie Algebras and Representation Theory

"An excellent introduction to the subject, ideal for a one semester graduate course."a "THE AMERICAN MATHEMATICAL MONTHLY

"Exceptionally well written and ideally suited either for independent reading or as a text for an introduction to Lie algebras and their representations."a "MATHEMATICAL REVIEWS

About the Author

James E. Humphreys was born in Erie, Pennsylvania, and received his AB from Oberlin College, Ohio in 1961, and his PhD from Yale University, Connecticut in 1966. He has taught at the University of Oregon, Courant Institute of Mathematical Sciences, New York University, and the University of Massachusetts, Amherst (now retired). He visits the Institute of Advanced Studies, Princeton and Rutgers. He is the author of several graduate texts and monographs.
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Product Details

  • Series: Graduate Texts in Mathematics (Book 9)
  • Hardcover: 173 pages
  • Publisher: Springer (October 27, 1994)
  • Language: English
  • ISBN-10: 0387900535
  • ISBN-13: 978-0387900537
  • Product Dimensions: 6.1 x 0.5 x 9.2 inches
  • Shipping Weight: 15.5 ounces (View shipping rates and policies)
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #472,180 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on August 8, 2001
Format: Hardcover
This book is a pretty good introduction to the theory of Lie algebras and their representations, and its importance cannot be overstated, due to the myriads of applications of Lie algebras to physics, engineering, and computer graphics. The subject can be abstract, and may at first seem to have minimal applicability to beginners, but after one gets accustomed to thinking in terms of the representations of Lie algebras, the resulting matrix operations seem perfectly natural (and this is usually the approach taken by physicists). The book is aimed at an audience of mathematicians, and there is a lot of material covered, in spite of the size of the book. Readers who desire an historical approach should probably supplement their reading with other sources. Readers are expected to have a strong background in linear and abstract algebra, and the book as a textbook is geared toward graduate students in mathematics. Only semisimple Lie algebras over algebraically closed fields are considered, so readers interested in Lie algebras over prime characteristic or infinite-dimensional Lie algebras (such as arise in high energy physics), will have to look elsewhere. Physicists can profit from the reading of this book but close attention to detail will be required.
The first chapter covers the basic definitions of Lie algebras and the algebraic properties of Lie algebras. No historical motivation is given, such as the connection of the theory with Lie groups, and Lie algebras are defined as vector spaces over fields, and not in the general setting of modules over a commutative ring. The four classical Lie algebras are defined, namely the special linear, symplectic, and orthogonal algebras.
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Format: Hardcover
Humphreys' book on Lie algebras is rightly considered the standard text. Very thorough, covering the essential classical algebras, basic results on nilpotent and solvable Lie algebras, classification, etc. up to and including representations. Don't let the relatively small number of pages fool you; the book is quite dense, and so even covering the first 30 pages is a nice accomplishment for a student. Small caveat, the notation might be a bit confusing until you get used to it, but this is a common problem due to having both a Lie and a matrix product floating around, and is not a fault of the text. There is also a nice selection of exercises, between 5 and 10 per section.
Highly recommended; every mathematician should know the basics of Lie algebras.
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Format: Hardcover
I must admit, my progress through this book can be measured in lines. It's not that it's confusing, but that it's pretty dense. The proofs are structured in such a way as to leave teasing amount of details to the reader, and the text measures understanding as much as the exercises. It is that which makes reading this book worthwhile.

From an academic point of view, the material in this book is very standard. The content of the first four chapters is closely paralleled by an introductory graduate level course in Lie Algebra and Representation Theory at MIT (although the instructor did not explicitly declare this as class text.) In many ways, this book is my ticket out of attending lectures, and it has done a great job so far.

I must admit that it can be frustrating at times to work out the statements of the proofs, but it only makes the understanding just that much more pleasant and adds the perfect amount of emotion to an otherwise black/white text.
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Format: Hardcover
I am completely mystified about why anyone likes this book, let alone why anyone would think it's a good way to learn this material. The exposition is badly organized--all trees and no forest--and the proofs are ugly and unintuitive, due mostly to Humphreys' decision to "minimize prerequisites."

It's true that Humphreys covers more topics than Serre does, and I imagine this is the main reason this book is the standard text. But there is no shortage of lecture notes available for free on whatever additional topics are needed to supplement Serre.
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Format: Paperback Verified Purchase
Moves at an advanced pace, but doesn't skip any major steps in any arguments. The exercises make you think about the material.
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