# .

# Sophus Lie

Marius Sophus Lie (Norwegian pronunciation: [liː] "Lee") (17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous symmetry, and applied it to the study of geometry and differential equations.

Biography

Sophus Lie was born in Nordfjordeid, Norway, the youngest of six children. As a young man, he intended to pursue a military career, but due to his myopia, he instead became a student at the University of Oslo.[1]

He obtained his Ph.D. at that university in 1872, with a thesis entitled On a class of geometric transformations.[2]

He was made Honorary Member of the London Mathematical Society in 1878, Member of the French Academy of Sciences in 1892, Fellow of the Royal Society of London in 1895 and foreign associate of the National Academy of Sciences of the United States of America in 1895.

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.[3][4]

Sophus Lie died at the age of 56, due to pernicious anemia, a disease caused by impaired absorption of vitamin B12.[3]

Hermann Weyl used Lie's work on group theory in his papers from 1922 and 1923, and Lie's groups today play a role in quantum mechanics.[4]

Seminar Sophus Lie

Seminar Sophus Lie is an international seminar of mathematicians interested in the theory of Lie groups and their wider horizon. It was founded around 1990 when, during the Volkskammer Government of the German Democratic Republic in 1989, open contact between mathematicians in East and West Germany became possible for the first time since 1961. Several mathematicians located at the Technische Hochschule Darmstadt, the University of Erlangen, the University of Greifswald, and the University of Leipzig informally organized the Seminar, with financial support by the Deutsche Forschungsgemeinschaft. The first meeting happened at the University of Leipzig, in January 1991. Since then, the Seminar has usually met once a semester. Over the years, the Seminar has gained participants from all over Europe.[5]

See also

* Lie bracket

* Lie derivative

* Lie sphere geometry

* Lie's third theorem

* Carathéodory-Jacobi-Lie theorem

Notes

1. ^ O'Connor, JJ; Robertson, EF. "Marius Sophus Lie". http://www-history.mcs.st-andrews.ac.uk/Biographies/Lie.html. Retrieved 2009-01-23.

2. ^ "M. Sophus (Marius) Lie". Mathematics Genealogy Project. http://genealogy.math.ndsu.nodak.edu/id.php?id=18235. Retrieved 2009-01-23.

3. ^ a b Helgason, Sigurdur (1994). "Sophus Lie, the Mathematician". Proceedings of The Sophus Lie Memorial Conference, Oslo, August, 1992. Oslo: Scandinavian University Press. pp. 3–21. http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-755Fall-2004/FFB7FE51-3ABA-4EF9-A0A9-CDFF32C4372C/0/helga_sopmath3_2.pdf.

4. ^ a b Gale, Thomson. "Marius Sophus Lie Biography". World of Mathematics. http://www.bookrags.com/biography/marius-sophus-lie-wom/. Retrieved 2009-01-23.

5. ^ "Seminar Sophus Lie". http://math.ubbcluj.ro/~aga_team/SophusLie/. Retrieved 2009-01-23.

External links

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