This book describes the life and achievements of the great French mathematician, Elie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential equations, and differential geometry, as well of later developments stemming from his ideas. There is also a biographical sketch of Cartan's life. A monumental tribute to a towering figure in the history of mathematics, this book will appeal to mathematicians and historians alike.

Readership

Graduate students, mathematicians, and historians.

Reviews

"Provide[s] a broad and clear overview of the mathematics leading to, and growing out of, the work of Cartan. For anyone wishing to understand something of Cartan's mathematics and its historical context, this book will provide a good starting point and a continuing helpful reference work ... the authors have performed an invaluable service for anyone interested in what Cartan achieved and how it relates to subsequent developments."

-- Historia Mathematica

Table of Contents

• The life and the work of É. Cartan
• Lie groups and algebras
• Projective spaces and projective metrics
• Lie pseudogroups and Pfaffian equations
• The method of moving frames and differential geometry
• Riemannian manifolds. Symmetric spaces
• Generalized spaces
• Appendix A. Rapport sur les travaux de M. Cartan by H. Poincaré
• Appendix B. Sur une dégénérescence de la géométrie euclidienne
• Appendix C. Allocution de M. Élie Cartan
• Appendix D. The influence of France in the development of mathematics
• Bibliography