title: Essays in the History of Lie Groups and Algebraic Groups (History of Mathematics, V. 21)
author:  Armand Borel 
description: "The book under review was written by a leading contributor to the development of the theory of Lie and algebraic groups during the second half of the 20th century ... Borel's work stands out ... by virtue of its genuinely scholarly nature ... perceptive essays ... Chapter 4 on E. Cartan's theory of symmetric spaces is notable for its detailed analysis of Cartan's main papers on the subject ... future historians interested in the interplay of Lie groups and differential geometry will find this essay an invaluable entre to Cartan's mathematics ... Chapter 5 ... is especially notable for the new insights it provides into the work of Ludwig Maurer ... many historians will benefit greatly from the expertise and insights contained in Borel's thoughtful, carefully written essays." ---- Centaurus, International Magazine of the History of Mathematics, Science and Technology<br /><br />"The exposition in this book is given in a fascinating and understandable language ... the book is useful for specialists as well as for people interested in the history of the development of the theory." ---- Mathematica Bohemica<br /><br />"The book is an essential contribution to the conmprhension of the central position taken by Lie group theory ... It should be read by any perosn wanting to learn about the cultural interest of mathematics because it is written by one of the most important actors in the field ..." ---- Zentralblatt MATH
zlib_text: 
  
  
  ![Cover Image](images/0486445291.jpg)
  
  
  
  
  
  LIE GROUPS, LIE ALGEBRAS, AND SOME OF THEIR APPLICATIONS
  
  
  Robert Gilmore
  
  
  Drexel University
  
  
  DOVER PUBLICATIONS, INC.
  
  
  Mineola, New York
  
  
  Copyright
  
  
  Copyright © 1974, 2002 by Robert Gilmore
  
  
  All rights reserved.
  
  
  Bibliographical Note
  
  
  This Dover edition, first published in 2005, is an unabridged republication of
  the work published by John Wiley & Sons, Inc., New York, 1974.
  
  
  International Standard Book Number: 0-486-44529-1
  
  
  Manufactured in the United States of America  
  Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501
  
  
  _Preface_
  
  
  Only a century has elapsed since 1873, when Marius Sophus Lie began his
  research on what has evolved into one of the most fruitful and beautiful
  branches of modern mathematics—the theory of Lie groups. These researches
  culminated twenty years later with the publication of landmark treatises by S.
  Lie and F. Engel [1–3] between 1888 and 1893, and by W. Killing [1–4] from
  1888 to 1890. 