Emergence of the Theory of Lie Groups - Thomas Hawkins - Springer Hardcover

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“Publisher: SpringerYear: 2000ISBN: 0387989633Description: Hardcover without dust jacket, Fine ...
ISBN
9780387989631
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Product Identifiers

Publisher
Springer New York
ISBN-10
0387989633
ISBN-13
9780387989631
eBay Product ID (ePID)
1670426

Product Key Features

Number of Pages
Xiii, 566 Pages
Language
English
Publication Name
Emergence of the Theory of Lie Groups : an Essay in the History of Mathematics, 1869-1926
Publication Year
2000
Subject
Group Theory, Algebra / Abstract, History & Philosophy
Type
Textbook
Subject Area
Mathematics
Author
Thomas Hawkins
Series
Sources and Studies in the History of Mathematics and Physical Sciences Ser.
Format
Hardcover

Dimensions

Item Height
0.5 in
Item Weight
76.9 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
99-056073
Reviews
"....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, "....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
Dewey Edition
21
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512/.55
Table Of Content
I: Sophus Lie.- 1. The Geometrical Origins of Lie's Theory.- 2. Jacobi and the Analytical Origins of Lie's Theory.- 3. Lie's Theory of Transformation Groups 1874-1893..- II: Wilhelm Killing.- 4. The Background to Killing's Work on Lie Algebras.- >Chapter 5. Killing and the Structure of Lie Algebrass.- III: Élie Cartan.- 6. The Doctoral Thesis of Élie Cartan.- 7. Lie's School & Linear Representations.- 8. Cartan's Trilogy: 1913-14.- IV: Hermann Weyl.- 9. The Göttingen School of Hilbert.- 10. The Berlin Algebraists: Frobenius & Schur.- 11. From Relativity to Representations.- 12. Weyl's Great Papers of 1925 and 1926.- Afterword. Suggested Further Reading.- References. Published & Unpublished Sources.
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., Lie groups and Lie algebras arose in the study of the mathematical properties of rotations. The ideas were originally developed by the Norwegian mathematician Sophus Lie (1849-1899), and they play an important role in the development of 20th century mathematics and mathematical physics. This book focuses on the origins and subsequent development of the structure of the theory, particularly the structure and representations of semisimple groups, with particular emphasis on the motivation behind the mathematics. It should thus be useful not only to historians of mathematics and to mathematicians interested in the history of their field, but also to students., 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., 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.
LC Classification Number
QA174-183

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