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

by Thomas Hawkins
     
 

ISBN-10: 0387989633

ISBN-13: 9780387989631

Pub. Date: 07/01/2000

Publisher: Springer New York

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

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Overview

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.

Product Details

ISBN-13:
9780387989631
Publisher:
Springer New York
Publication date:
07/01/2000
Series:
Sources and Studies in the History of Mathematics and Physical Sciences Series
Edition description:
2000
Pages:
566
Product dimensions:
6.40(w) x 9.40(h) x 1.50(d)

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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