## Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869–1926This book is both more and less than a history of the theory of Lie groups during the period 1869-1926. No attempt has been made to provide an exhaustive treatment of all aspects of the theory. Instead, I have focused upon its origins and upon the subsequent development of its structural as pects, particularly the structure and representation of semisimple groups. In dealing with this more limited subject matter, considerable emphasis has been placed upon the motivation behind the mathematics. This has meant paying close attention to the historical context: the mathematical or physical considerations that motivate or inform the work of a particular mathematician as well as the disciplinary ideals of a mathematical school that encourage research in certain directions. As a result, readers will ob tain in the ensuing pages glimpses of and, I hope, the flavor of many areas of nineteenth and early twentieth century geometry, algebra, and analysis. They will also encounter many of the mathematicians of the period, includ ing quite a few not directly connected with Lie groups, and will become acquainted with some of the major mathematical schools. In this sense, the book is more than a history of the theory of Lie groups. It provides a different perspective on the history of mathematics between, roughly, 1869 and 1926. Hence the subtitle. |

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### Contents

Jacobi and the Analytical Origins of Lies Theory | 43 |

Lies Theory of Transformation Groups 18741893 | 75 |

Wilhelm Killing | 87 |

The Background to Killings Work | 100 |

Killing and the Structure of Lie Algebrass | 138 |

Elie Cartan | 182 |

Lies School Linear Representations | 225 |

191314 | 277 |

### Other editions - View all

Emergence of the Theory of Lie Groups: An Essay in the History of ... Thomas Hawkins Limited preview - 2000 |

Emergence of the Theory of Lie Groups: An Essay in the History of ... Thomas Hawkins No preview available - 2012 |

### Common terms and phrases

abelian adjoint group Berlin Cartan classification Clebsch coefficients complete reducibility theorem considered contact transformations continuous groups coordinates corresponding covariant Darboux defined denote developed dimension dissertation elementary divisors elements Engel Erlanger Programm essay finite groups follows foundations of geometry Frobenius function fundamental GL(n Göttingen Hilbert homogeneous homogeneous coordinates Hurwitz ideas infinitesimal transformations integral irreducible representations isomorphic Jacobi Jacobi identity Killing Killing's theory Klein Kowalewski leave nothing planar lectures Leipzig letter Lie algebras Lie groups Lie's theory line geometry linear transformations manifold mathematical mathematicians method multiplicity non-Euclidean geometry notation orthogonal paper partial differential equations Picard planar invariant Poincaré polynomial problem of determining projective groups proof properties rank zero realized Riemann satisfying Schur secondary roots Section semisimple groups simple groups sl(n solvable space forms structure Study subalgebra subgroup symmetric tensor theory of groups theory of invariants tion transformation groups variables vector Weierstrass weight Weyl Weyl's