文件名称：The Erlangen Program and Its Impact in Mathematics and Physics
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更新时间：2021-05-09 09:00:41
math, The Erlangen Program
The Erlangen program provides a fundamental point of view on the place of trans- formation groups in mathematics and physics. Felix Klein wrote the program, but Sophus Lie also contributed to its formulation, and his writings are probably the best example of how this program is used in mathematics. The present book gives the first modern historical and comprehensive treatment of the scope, applications and impact of the Erlangen program in geometry and physics and the roles played by Lie and Klein in its formulation and development. The book is also intended as an introduc- tion to the works and visions of these two mathematicians. It addresses the question of what is geometry, how are its various facets connected with each other, and how are geometry and group theory involved in physics. Besides Lie and Klein, the names of Bernhard Riemann, Henri Poincare ́, Hermann Weyl, E ́lie Cartan, Emmy Noether and other major mathematicians appear at several places in this volume.