Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century



Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century
Publisher: Birkhauser | ISBN: 0817633162 | edition 1988 | DJVU | 251 pages | 6,5 mb

Starting with Galois and his contribution to the evolving subject of group theory Yaglom gives a beautiful account of the lives and works of the major players in the development of the subject in the nineteenth century: Jordan, who was a teacher of Lie and Klein in Paris and their adventures during the Franco-Prussian War. Monge and Poncelet developing projective geometry as well as Bolyai, Gauss and Lobachevsky and their discovery of hyperbolic geometry. Riemann's contributions and the development of modern linear Algebra by Grassmann, Cayley and Hamilton are described in detail. The last two chapters are devoted to Lie's development of Lie Algebras and his construction of the geometry from a continuous group and Klein's Erlanger Programm unifying the different approaches to geometry by emphasizing automorphism groups.

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