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Sophus Lie and Felix Klein: The Erlangen Program and Its Impact in Mathematics and Physics
IRMA Lectures in Mathematics and Theoretical Physics Vol. 23

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

Lizhen Ji (University of Michigan, Ann Arbor, USA)
Athanase Papadopoulos (Université de Strasbourg, France)

ISBN print 978-3-03719-148-4, ISBN online 978-3-03719-648-9
DOI 10.4171/148
April 2015, 348 pages, hardcover, 17.0 x 24.0 cm.
48.00 Euro

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.

Keywords: Sophus Lie, Felix Klein, the Erlangen program, group action, Lie group action, symmetry, projective geometry, non-Euclidean geometry, spherical geometry, hyperbolic geometry, transitional geometry, discrete geometry, transformation group