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An Introduction to Lie Groups and Lie Algebras (Cambridge Studies in Advanced Mathematics) 1st Edition

4.0 out of 5 stars 3 customer reviews
ISBN-13: 978-0521889698
ISBN-10: 0521889693
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Editorial Reviews

Review

"The book is a very concise and nice introduction to Lie groups and Lie algebras. It seems to be well suited for a course on the subject. The exercises and examples will be useful in that case."
Erik Koelink, Mathematical Reviews

"I strongly recommend this book as a possible selection for graduate course(s), as well as independent study, or individual reading."
Mihaela Poplicher, MAA Reviews

Book Description

This graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style, this is a contemporary introduction to the subject. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras.
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Product Details

  • Series: Cambridge Studies in Advanced Mathematics (Book 113)
  • Hardcover: 236 pages
  • Publisher: Cambridge University Press; 1 edition (September 1, 2008)
  • Language: English
  • ISBN-10: 0521889693
  • ISBN-13: 978-0521889698
  • Product Dimensions: 6 x 0.7 x 9 inches
  • Shipping Weight: 14.9 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #1,200,792 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Hardcover
I used this book as the primary text for an introductory course on Lie groups and Lie algebras. There are several aspects of the book which distinguish it from every other book on the same topic, making it an indespensable resource for the beginning student.

First, the book is, as its title indicates, an introduction, and a fairly brief one at that. It is not intended to be comprehensive in scope or in depth, rather to gently introduce some fairly complex ideas in the most basic way possible. This is the primary reason it is so useful to start with: The author knows just how much detail is necessary and skips cumbersome and unenlightening proofs. For example, he doesn't prove Serre's theorem or finish the proof of the PBW theorem, but rather refers to other books for these. In contrast to other books on the subject, the student doesn't have to sift the important points from the nitty-gritty details. Every section is important and worth reading. I particularly appreciate that the sections on Lie groups don't require that the reader is an expert in differential geometry and reviews all essential prerequisites.

Of particular value is the excellent collection of exercises. The majority of these are not particularly difficult, but most are enormously worthwhile. Having done lots of exercises from other books, including Knapp (Lie groups beyond an introduction), Hall, Humphreys, and others, I can safely say these are among the best, reaching both an optimal level of difficulty and a fair balance between computation and theory. (Note: Hall's book has great exercises too and are good for those who want more practice with computations).
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Format: Hardcover
this is a wickedly good book. it's concise (yeah!) and it's well written. it misses out on lots of stuff (spin representations, etc..). but once you read this book you will have the formalism down pat, and then everything else becomes easy.

if you put in the hours to read this book cover to cover -- like sitting down for 3 days straight 8 hours a day, then will learn the stuff. if you don't persevere and get overwhelmed with the stuff that is not clear at the beginning, then you will probably chuck it out the window.

lie groups and lie algebras in 200 pages done in an elegant way that doesn't look like lecture notes cobbled together is pretty impressive.
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Format: Hardcover Verified Purchase
It is trying too hard to be a rigorous introduction without mentioning the differential topology behind everything. It is clear that it assumes a background in differential topology but every time a proof involves stepping in that direction it is omitted.7 When you get to the exercises there are many that would be good, albeit very long, if there was more differential topology. It is fine to sweep many of the rigorous technical details under the rug, and needed to get to the juicy part of the subject, but craft the exercises to avoid such details as well. Once the book switches to Lie algebras and representations it does clean up its act a bit. There is also a glaring omission of maximal tori (or Borel subgroups) which are essential in any further study.
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