Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926 / Edition 1

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Lie groups arose in the study of the mathematical properties of rotati ons; like physical rotations, they depend on a parameter (such as the angle of rotation) that can be varied in a continuous manner, and like rotations in more than 2 dimensions (whose result depends on the orde r in which they are performed), they form a non-commutative group; the derivative of the elements with respect to the parameter gives rise t o a set of operators whose algebraic properties are themselves of inte rest: the Lie algebra. These ideas can of course be generalized to oth er physical transformations, and they play an important role in the de velopment of 20th century mathematics and mathematical physics.

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Editorial Reviews

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"....this study is just as clearly a stunning achievement. Few historians of mathematics have made a serious attempt to cross the bridge joining the nineteenth and twentieth centuries, and those who have made the journey have tended to avert their eyes from the mainstream traffic....the single greatest merit of Hawkins' book is that the author tries to place the reader in the middle of the action, offering a close up look at how mathematics gets made...Hawkins' account of this strange but wonderful saga resurrects a heroic chapter in the history of mathematics. For anyone with a serious interest in the rich background developments that led to modern Lie theory, this book should be browsed, read, savored, and read again."

-Notices of the AMS

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Product Details

Table of Contents

Preface.- The Geometrical Origins of Lie's theory.- Jacobi & The Analytical Origins of Lie's Theory.- Lie's Theory of Transformation Groups 1874-1893.- Non-euclidean Geometry & Weierstrassian Mathematics.- Killing & the Structure of Lie Algebras.- The Doctoral Thesis of Elie Cartan.- Lie's School & Linear Representations.- Cartan's Trilogy: 1913-14.- The Göttingen School of Hilbert.- The Berlin Algebraists: Frobenius & Schur.- From Relativity to Representations.- Weyl's Great Papers of 1925 & 1926.- References.- Index.

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