**Marius Sophus Lie** (IPA pronunciation: [liː], pronounced "Lee") (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. Image File history File links No higher resolution available. ...
December 17 is the 351st day of the year (352nd in leap years) in the Gregorian calendar. ...
1842 was a common year starting on Saturday (see link for calendar). ...
The small village of Nordfjordeid is the administrative capital of the municipality of Eid, in Sogn og Fjordane county, southwest Norway. ...
February 18 is the 49th day of the year in the Gregorian calendar. ...
Year 1899 (MDCCCXCIX) was a common year starting on Sunday (link will display the full calendar). ...
County Oslo NO-03 District Viken Municipality NO-0301 Administrative centre Oslo Mayor (2004) Per Ditlev-Simonsen (H) Official language form BokmÃ¥l Area - Total - Land - Percentage Ranked 224 454 kmÂ² 426 kmÂ² 0. ...
Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
The University of Oslo (in Norwegian Universitetet i Oslo, in Latin Universitas Osloensis) was founded in 1811 as Universitas Regia Fredericiana (the Royal Frederick University, in Norwegian Det Kongelige Frederiks Universitet). ...
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. ...
Articles with similar titles include the NATO phonetic alphabet, which has also informally been called the â€œInternational Phonetic Alphabetâ€. For information on how to read IPA transcriptions of English words, see IPA chart for English. ...
December 17 is the 351st day of the year (352nd in leap years) in the Gregorian calendar. ...
1842 was a common year starting on Saturday (see link for calendar). ...
February 18 is the 49th day of the year in the Gregorian calendar. ...
Year 1899 (MDCCCXCIX) was a common year starting on Sunday (link will display the full calendar). ...
Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ...
In mathematics, continuous symmetry is an intuitive idea corresponding to the concept of viewing some symmetries as motions, as opposed to e. ...
Calabi-Yau manifold Geometry (Greek Î³ÎµÏ‰Î¼ÎµÏ„ÏÎ¯Î±; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ...
In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ...
He obtained his Ph.D. at the University of Christiania in 1872, with a thesis entitled *On a class of geometric transformations*. The University of Oslo (in Norwegian Universitetet i Oslo, in Latin Universitas Osloensis) was founded in 1811 as Universitas Regia Fredericiana (the Royal Frederick University, in Norwegian Det Kongelige Frederiks Universitet). ...
He was made Honorary Member of the London Mathematical Society in 1878 and Fellow of the Royal Society (FRS). The London Mathematical Society (LMS) is the leading mathematical society in England. ...
The premises of The Royal Society in London (first four properties only). ...
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. In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ...
In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie (IPA pronunciation: , sounds like Lee), is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. ...
Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ...
In mathematics, a Lie group is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. ...
In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ...
In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. ...
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. ...
## See also
In mathematics, E8 is the name of a root system, a particular configuration of vectors in Euclidean space of high dimension, and of several associated mathematical objects. ...
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. ...
In mathematics, a Lie derivative, named after Sophus Lie, is a derivation on the algebra of tensor fields over a manifold M. The vector space of all Lie derivatives on M forms an infinite dimensional Lie algebra with respect to the Lie bracket defined by The Lie derivatives are represented...
In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie (IPA pronunciation: , sounds like Lee), is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. ...
The CarathÃ©odory-Jacobi-Lie theorem is a theorem in symplectic topology which generalizes Darbouxs theorem. ...
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