Sophus Lie

From Wikipedia, the free encyclopedia

Marius Sophus Lie (December 17, 1842 - February 18, 1899) was a Norwegian-born mathematician. He largely created the theory of continuous symmetry, and applied it to the study of geometry and differential equations.

Lie's principal tool, and one of his greatest achievements, was the discovery that continuous transformation groups (now called after him Lie groups) could be better understood by "linearizing" them, and studying the corresponding generating vector fields (the so-called infinitesimal generators). The generators are subject to a linearized version of the group law, now called the commutator bracket, and have the structure of what is today called a Lie algebra.

[edit] See also

• Lie algebra
• Lie derivative
• Lie group
• Carathéodory-Jacobi-Lie theorem

[edit] External links

• O'Connor, John J., and Edmund F. Robertson. "Sophus Lie". MacTutor History of Mathematics archive.