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

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.