Ji L., Papadopoulos A. (Eds.) Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics

European Mathematical Society, 2015. — 348 p. – (IRMA Lectures in Mathematics and Theoretical Physics 23). — ISBN: 978-3-03719-148-4.The Erlangen program expresses a fundamental point of view on the use of groups and transformation groups in mathematics and physics. This 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, including Hermann Weyl, Élie Cartan, Henri Poincaré, and many others. All these facets of the Erlangen program appear in this volume. The book is written by well-known experts in geometry, physics and the history of mathematics and physics.Sophus Lie, a giant in mathematics
Felix Klein: his life and mathematics
Klein and the Erlangen Programme
Klein’s “Erlanger Programm”: do traces of it exist in physical theories?
On Klein’s So-called Non-Euclidean geometry
What are symmetries of PDEs and what are PDEs themselves?
Transformation groups in non-Riemannian geometry
Transitional geometry
On the projective geometry of constant curvature spaces
The Erlangen program and discrete differential geometry
Three-dimensional gravity – an application of Felix Klein’s ideas in physics
Invariances in physics and group theory