Emergence of the Theory of Lie Groups

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.

Zusammenfassung
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.

Inhalt
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 18741893..- 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: 191314.- 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 Published & Unpublished Sources.

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