Thomas Hawkins

Emergence of the Theory of Lie Groups (eBook, PDF)

An Essay in the History of Mathematics 1869-1926

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 566
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461212027
• Artikelnr.: 43993269

Autorenporträt

Thomas Hawkins won the 2001 Whiteman Prize, an AMS prize that honors notable exposition in the history of mathematics. The citation for the prize calls Hawkins "an outstanding historian of mathematics whose current research and numerous publications display the highest standards of mathematical and historical sophistication."  The citation also mentions a number of Hawkins' works, including his book, The Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926.  "Hawkins' work has truly transformed our understanding of how modern mathematics has evolved," the citation concludes.

Inhaltsangabe

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 Published & Unpublished Sources.

Rezensionen

"....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