Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics
| Authors | Ji, Lizhen Papadopoulos, Athanase |
| Series | IRMA Lectures in Mathematics and Theoretical Physics [23.0] |
| Tags | Projective Geometry, Felix Klein -- 1849-1925, geometry, MATHEMATICS / Geometry / General, Geometry -- History, Sophus Lie -- 1842-1899, General, Geometric group theory, Transformation groups, mathematical physics, Differential Geometry, Mathematics, Lie groups |
| Publisher | European Mathematical Society |
| Published | 15 dic 2015 |
| Date | 20 dic 2017 |
| Languages | eng |
| Identifiers | oclc: 919632244, isbn: 9783037196489, uri: http://ams.rice.edu/mathscinet-getitem?mr=3379703, google: FMCdjwEACAAJ |
| Formats |
Description
The Erlangen program expresses a fundamental point of view on the use of groups and transformation groups in mathematics and physics. The present volume is the first modern comprehensive book on that program and its impact in contemporary mathematics and physics. Klein spelled out the program, and Lie, who contributed to its formulation, is the first mathematician who made it effective in his work. The theories that these two authors developed are also linked to their personal history and to their relations with each other and with other mathematicians, incuding Hermann Weyl, Élie Cartan, Henri Poincaré, and many others. All these facets of the Erlangen program appear in the present volume. The book is written by well-known experts in geometry, physics and history of mathematics and physics. It is addressed to mathematicians, to graduate students, and to all those interested in the development of mathematical ideas.
Papers in this collection include the following:
Lizhen Ji and Athanase Papadopoulos, "Introduction”, xi–xviii.
Lizhen Ji, "Sophus Lie, a giant in mathematics”, 1–26. MR3362210
Lizhen Ji, "Felix Klein: his life and mathematics”, 27–58. MR3362211
Jeremy J. Gray, "Klein and the Erlangen Programme”, 59–73. MR3362212
Hubert Goenner, "Klein's "Erlanger Programm”: do traces of it exist in physical theories?'', 77–90. MR3362213
Norbert A'Campo and Athanase Papadopoulos, "On Klein's so-called non-Euclidean geometry”, 91–136. MR3362214
Alexandre Vinogradov, "What are symmetries of PDEs and what are PDEs themselves?”, 137–190. MR3362215
Charles Frances, "Transformation groups in non-Riemannian geometry”, 191–216. MR3362216
Norbert A'Campo and Athanase Papadopoulos, "Transitional geometry”, 217–235. MR3362217
Athanase Papadopoulos and Sumio Yamada, "On the projective geometry of constant curvature spaces”, 237–245. MR3362218
Yuri B. Suris, "The Erlangen program and discrete differential geometry”, 247–279. MR3362219
Catherine Meusburger, "Three-dimensional gravity—an application of Felix Klein's ideas in physics”, 283–306. MR3362220
Jean-Bernard Zuber, "Invariances in physics and group theory”, 307–326. MR3362221.