Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics [electronic resource] /
Lizhen Ji, Athanase Papadopoulos
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2015
- 1 online resource (348 pages)
- IRMA Lectures in Mathematics and Theoretical Physics (IRMA) 23 .
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 / Lizhen Ji -- Lizhen Ji -- Jeremy J. Gray -- Hubert Goenner -- Norbert A’Campo, Athanase Papadopoulos -- Alexandre Vinogradov -- Charles Frances -- Norbert A’Campo, Athanase Papadopoulos -- Athanase Papadopoulos, Sumio Yamada -- Yuri B. Suris -- Catherine Meusburger -- Jean-Bernard Zuber.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037196489
10.4171/148 doi
History of mathematics
Geometry
History and biography
Topological groups, Lie groups
Geometry
Differential geometry
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 / Lizhen Ji -- Lizhen Ji -- Jeremy J. Gray -- Hubert Goenner -- Norbert A’Campo, Athanase Papadopoulos -- Alexandre Vinogradov -- Charles Frances -- Norbert A’Campo, Athanase Papadopoulos -- Athanase Papadopoulos, Sumio Yamada -- Yuri B. Suris -- Catherine Meusburger -- Jean-Bernard Zuber.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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.
9783037196489
10.4171/148 doi
History of mathematics
Geometry
History and biography
Topological groups, Lie groups
Geometry
Differential geometry