Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869–1926 (Sources and Studies in the History of Mathematics and Physical Sciences) - Hardcover

Hawkins, Thomas

Hardcover

ISBN 10: 0387989633 ISBN 13: 9780387989631

Publisher: Springer, 2000

Synopsis

This book is both more and less than a history of the theory of Lie groups during the period 1869-1926. No attempt has been made to provide an exhaustive treatment of all aspects of the theory. Instead, I have focused upon its origins and upon the subsequent development of its structural as­ pects, particularly the structure and representation of semisimple groups. In dealing with this more limited subject matter, considerable emphasis has been placed upon the motivation behind the mathematics. This has meant paying close attention to the historical context: the mathematical or physical considerations that motivate or inform the work of a particular mathematician as well as the disciplinary ideals of a mathematical school that encourage research in certain directions. As a result, readers will ob­ tain in the ensuing pages glimpses of and, I hope, the flavor of many areas of nineteenth and early twentieth century geometry, algebra, and analysis. They will also encounter many of the mathematicians of the period, includ­ ing quite a few not directly connected with Lie groups, and will become acquainted with some of the major mathematical schools. In this sense, the book is more than a history of the theory of Lie groups. It provides a different perspective on the history of mathematics between, roughly, 1869 and 1926. Hence the subtitle.

About this title

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.

Edition details

• Publisher: Springer
• Publication date: 2000
• Language: English
• ISBN 10: 0387989633
• ISBN 13: 9780387989631
• Binding: Hardcover
• Number of pages: 579