Emergence of the Theory of Lie Groups [Hardcover]

Thomas Hawkins (Author)

Book Description

ISBN-10: 0387989633 | ISBN-13: 978-0387989631 | Publication Date: July 19, 2000 | Edition: 1

The great Norwegian mathematician Sophus Lie developed the general theory of transformations in the 1870s, and the first part of the book properly focuses on his work. In the second part the central figure is Wilhelm Killing, who developed structure and classification of semisimple Lie algebras. The third part focuses on the developments of the representation of Lie algebras, in particular the work of Elie Cartan. The book concludes with the work of Hermann Weyl and his contemporaries on the structure and representation of Lie groups which serves to bring together much of the earlier work into a coherent theory while at the same time opening up significant avenues for further work.

Editorial Reviews

Review

"....this study is just as clearly a stunning achievement. Few historians of mathematics have made a serious attempt to cross the bridge joining the nineteenth and twentieth centuries, and those who have made the journey have tended to avert their eyes from the mainstream traffic....the single greatest merit of Hawkins' book is that the author tries to place the reader in the middle of the action, offering a close up look at how mathematics gets made...Hawkins' account of this strange but wonderful saga resurrects a heroic chapter in the history of mathematics. For anyone with a serious interest in the rich background developments that led to modern Lie theory, this book should be browsed, read, savored, and read again." -Notices of the AMS

From the Back Cover

Written by the recipient of the 1997 MAA Chauvenet Prize for mathematical exposition, this book tells how the theory of Lie groups emerged from a fascinating cross fertilization of many strains of 19th and early 20th century geometry, analysis, mathematical physics, algebra and topology. The reader will meet a host of mathematicians from the period and become acquainted with the major mathematical schools. The first part describes the geometrical and analytical considerations that initiated the theory at the hands of the Norwegian mathematician, Sophus Lie. The main figure in the second part is Weierstrass'student Wilhelm Killing, whose interest in the foundations of non-Euclidean geometry led to his discovery of almost all the central concepts and theorems on the structure and classification of semisimple Lie algebras. The scene then shifts to the Paris mathematical community and Elie Cartans work on the representation of Lie algebras. The final part describes the influential, unifying contributions of Hermann Weyl and their context: Hilberts Göttingen, general relativity and the Frobenius-Schur theory of characters. The book is written with the conviction that mathematical understanding is deepened by familiarity with underlying motivations and the less formal, more intuitive manner of original conception. The human side of the story is evoked through extensive use of correspondence between mathematicians. The book should prove enlightening to a broad range of readers, including prospective students of Lie theory, mathematicians, physicists and historians and philosophers of science.

Product Details

• Hardcover: 576 pages
• Publisher: Springer; 1 edition (July 19, 2000)
• Language: English
• ISBN-10: 0387989633
• ISBN-13: 978-0387989631
• Product Dimensions: 9.5 x 6.4 x 1.2 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,423,782 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars I'm in heaven, August 25, 2010

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KB (Rome, Italy) - See all my reviews

This review is from: Emergence of the Theory of Lie Groups (Hardcover)

I can't remember the last time I purchased a book that I have enjoyed so thoroughly. The day it arrived I read sixty pages in different parts of the book, mostly in the section on Hilbert and Weyl. There are so many branches of advanced mathematics that are tied together here in one place. These different branches, most developed since 1850, are taught as separate subjects nowadays. But in their development they were driven by a small group of scholars and geniuses in a few cities in Europe. I feel as though I'm in Berlin and Paris and Göttingen listening to these great minds as they share ideas, and as one branch of mathematics nourishes and stimulates another. One of the great ideas of Riemann and Hilbert and Weyl is the unity of mathematics, and also physics. This book recaptures that mystical and beautiful unity. I felt like all my Christmases came at once. It was so difficult to choose a section to read that I read many, and have now settled down to read the whole book carefully from cover to cover.