Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869–1926

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Springer Science & Business Media, Dec 6, 2012 - Mathematics - 566 pages
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.
 

Contents

Preface
1
Jacobi and the Analytical Origins of Lies Theory
43
Lies Theory of Transformation Groups 18741893
75
Wilhelm Killing
87
The Background to Killings Work
100
Killing and the Structure of Lie Algebrass
138
Élie Cartan
182
Lies School Linear Representations
225
191314
277
The Göttingen School of Hilbert
317
Frobenius Schur
372
From Relativity to Representations
420
Weyls Great Papers of 1925 and 1926
465
Afterword Suggested Further Reading
513
Index
547
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