Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics

Lizhen Ji; Athanase Papadopoulos

doi:10.4171/148

pp. 1–26
Sophus Lie, a giant in mathematics
Lizhen Ji
pp. 27–58
Felix Klein: his life and mathematics
Lizhen Ji
pp. 59–75
Klein and the Erlangen Programme
Jeremy J. Gray
pp. 77–90
Klein’s “Erlanger Programm”: do traces of it exist in physical theories?
Hubert Goenner
pp. 91–136
On Klein’s <i>So-called Non-Euclidean geometry</i>
Norbert A’CampoAthanase Papadopoulos
pp. 137–190
What are symmetries of PDEs and what are PDEs themselves?
Alexandre Vinogradov
pp. 191–216
Transformation groups in non-Riemannian geometry
Charles Frances
pp. 217–235
Transitional geometry
Norbert A’CampoAthanase Papadopoulos
pp. 237–245
On the projective geometry of constant curvature spaces
Athanase PapadopoulosSumio Yamada
pp. 247–281
The Erlangen program and discrete differential geometry
Yuri B. Suris
pp. 283–306
Three-dimensional gravity – an application of Felix Klein’s ideas in physics
Catherine Meusburger
pp. 307–324
Invariances in physics and group theory
Jean-Bernard Zuber