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Quantum Groups (Graduate Texts in Mathematics) Hardcover – December 1, 1994

ISBN-13: 978-0387943701 ISBN-10: 0387943706 Edition: 1995th

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Product Details

  • Series: Graduate Texts in Mathematics (Book 155)
  • Hardcover: 534 pages
  • Publisher: Springer; 1995 edition (December 1, 1994)
  • Language: English
  • ISBN-10: 0387943706
  • ISBN-13: 978-0387943701
  • Product Dimensions: 9.4 x 6.4 x 1.4 inches
  • Shipping Weight: 2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #822,654 in Books (See Top 100 in Books)

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9 of 9 people found the following review helpful By Chris Woodward on September 13, 2000
Format: Hardcover
This is a very well-written book covering not only quantum groups but also the connections with low-dimensional topology. When comparing the presentation in the book with other presentations in the literature I realized how much work the author put in trying to make the material accessible. Part I covers Hopf algebras and quantum SL(2). Part II covers the Yang-Baxter equation and its solutions (R-matrices) and Drinfeld's quantum double construction. Part III deals with the applications to low-dimensional topology, i.e., the construction of knot invariants via braided tensor categories, in particular the construction of the Jones-Conway polynomial. Part IV is an account of Drinfeld's treatment of the monodromy of the Knizhnik-Zamolodchikov equations. The last chapter discusses finite type knot invariants, and discusses Cartier's combinatorial version of Kontsevich's universal knot invariant.
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6 of 9 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on September 2, 2001
Format: Hardcover
This book is further evidence of the tremendous influence that quantum physics, especially quantum field theory and superstring theory, has had on modern mathematics. Very rich mathematical structures and simplified methods of proof have resulted from looking at mathematics from a quantum point of view. Because of the enormous success of viewpoint, examples being proofs of the Atiyah-Singer index theorem, the Jones polynomial, and the Seiberg-Witten equations, one could justify a rephrasing of the remark by Eugene Wigner and now speak of "the reasonable effectiveness of physics in mathematics".
The book gives a fine overview of a field that has only been around for a few decades, and is manifested by brilliant developments. Those who have worked with the Yang-Baxter equations from the theory of exactly solved models in statistical mechanics will see these equations come alive here in a much more general form. In addition, knot theorists and geometric topologists will appreciate the discussion of how their constructions can be cast in the tensor and tangle categories that are explained in detail in this book. The title of the book is a little strange, given that the structures treated are more specific than groups, but the author has explained well the theory of quantum groups, as is it is now referrred to in journal classification schemes.
An in-depth reading of the book is time-consuming, and no doubt the average reader will not read it from cover to cover but instead will peruse only the areas of immediate interest. Part One of the book is an overview of what the author calls quantum SL(2), which is an example of a Hopf algebra.
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0 of 1 people found the following review helpful By Michael Fitzpatrick on July 1, 2014
Format: Hardcover Verified Purchase
There is a ton of useful information but is very dryly written. This book is best used as a reference.
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