## Elie Cartan (1869-1951)This book describes the life and achievements of the great french mathematician, Élie Cartan. Here readers will find detailed descriptions of Cartan's discoveries in Lie groups and algebras, associative algebras, differential geometry, as well as later developments stemming from his ideas. The volume includes 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. |

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### Contents

Lie Groups and Algebras | 33 |

Projective Spaces and Projective Metrics | 87 |

Lie Pseudogroups and Pfaffian Equations | 125 |

Chapter t 5 The Method of Moving Frames and Differential | 145 |

Riemannian Manifolds Symmetric Spaces | 177 |

Generalized Spaces | 211 |

Conclusion | 235 |

List of Publications of Elie Cartan | 248 |

Appendix A Rapport sur les Travaux de M Cartan by H Poincare | 266 |

The Influence of France in the Development | 281 |

303 | |

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### Common terms and phrases

absolute affine connection C. R. Acad Cartan considered CEuvres completes complex numbers complex simple Lie continuous groups coordinates corresponding curvature curve defined differential geometry dimension dimensional Divers Dynkin graphs elements Elie Cartan elliptic espaces Euclidean space exterior differential field finite formulas functions G-structure Galois Gauthier-Villars geodesic geometrie differentielle group G group of motions Groupes de Lie groups of transformations Hermitian hyperplane hypersphere hypersurfaces imaginary infinitesimal integral invariant involution isomorphic isotropic Lectures Lie algebra linear group linear representations manifold Vp Math mathematicians mathematics matrices moving frames n-dimensional non-Euclidean noncompact normal octaves orthogonal paper parameters Paris Partie Pfaffian equations plane Poincare problem projective space pseudo-Riemannian pseudo-Riemannian manifold pseudogroups published quadratic form quadric quaternion real simple Lie Riemannian manifolds simple groups simple Lie groups space CP space Rn straight lines structure subgroup submanifolds surface symmetric Riemannian spaces symmetric spaces symplectic tangent space tensor theorem theory tions two-dimensional variables vectors vols

### References to this book

Optimization and Inverse Problems in Electromagnetism Marek Rudnicki,Slawomir Wiak Limited preview - 2003 |

Es war die Kühnheit meiner Gedanken: Der Mathematiker Sophus Lie Arild Stubhaug No preview available - 2003 |