Emergence of the Theory of Lie Groups

"...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

• 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 Published & Unpublished Sources.