Marius Sophus Lie (/liː/ LEE; Norwegian: [liː]; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous...

In mathematics, the mathematician Sophus Lie (/liː/ LEE) initiated lines of study involving integration of differential equations, transformation groups...

In differential geometry, the Lie derivative (/liː/ LEE), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including...

Sophus or Sofus is a male given name. Notable people with the given name include: Sophus Aars (1841–1931), Norwegian civil servant and writer Sophus Andersen...

fact, this is another way to state the Lie–Kolchin theorem. The result for Lie algebras was proved by Sophus Lie (1876) and for algebraic groups was proved...

In mathematics, the Lie product formula, named for Sophus Lie (1875), but also widely called the Trotter product formula, named after Hale Trotter, states...

has been extended far beyond these origins. Lie groups are named after Norwegian mathematician Sophus Lie (1842–1899), who laid the foundations of the...

concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of...

{\displaystyle [x,x]=x\times x=0} . Lie algebras were introduced to study the concept of infinitesimal transformations by Sophus Lie in the 1870s, and independently...

Lie point symmetry is a concept in advanced mathematics. Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order...

under Sophus Lie in the years 1888–1889, worked on the subject of classification of simple Lie groups, which was started by Wilhelm Killing. In 1892 Lie came...

subgroup Arithmetic group Dunkl operator Modular form Langlands program Sophus Lie (1842 – 1899) Wilhelm Killing (1847 – 1923) Élie Cartan (1869 – 1951)...

a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple Lie groups can...

circle or sphere. It was introduced by Sophus Lie in the nineteenth century. The main idea which leads to Lie sphere geometry is that lines (or planes)...

after Sophus Lie. Sophus Lie (1842 – 1899), a mathematician, is the eponym of all of the things (and topics) listed below. Carathéodory–Jacobi–Lie theorem...

1899, when its establishment was proposed by the Norwegian mathematician Sophus Lie when he learned that Alfred Nobel's plans for annual prizes would not...

all special functions and all their properties. In fact, Sophus Lie invented the theory of Lie groups when studying the symmetries of differential equations...

was the young Sophus Lie, who would later create a strange new science on the basis of these ideas, the theory of continuous symmetry. Lie once commented...

Herman Lie (1869 – 1951) was a Norwegian judge. He was a son of Fredrik Gill Lie (1833–1899), and brother of composer Sigurd Lie, nephew of Sophus Lie, and...

transformations was first given by Sophus Lie. This was at the heart of his work, on what are now called Lie groups and their accompanying Lie algebras; and the identification...

Isaak Moiseevich Yaglom (Russian: Исаа́к Моисе́евич Ягло́м; 6 March 1921 – 17 April 1988) was a Soviet mathematician and author of popular mathematics...

subsumes the concepts of versor and hyperbolic versor as the terminology of Sophus Lie has replaced that of Hamilton and Macfarlane. In particular, for each...

Ossian Bonnet's (1867) investigations on surfaces of constant curvatures, Sophus Lie (1879) found a way to derive new pseudospherical surfaces from a known...

One-parameter groups were introduced by Sophus Lie in 1893 to define infinitesimal transformations. According to Lie, an infinitesimal transformation is an...

algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals. The classification of real simple Lie algebras is...

field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or...

second half of 20th century) Cartan's or the Cartan-Lie theorem as it was proved by Élie Cartan. Sophus Lie had previously proved the infinitesimal version:...

adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as...

with positive weight. A Lie subalgebra of g {\displaystyle {\mathfrak {g}}} containing a Borel subalgebra is called a parabolic Lie algebra. Hyperbolic group...

complex Lie groups. Real forms of complex semisimple Lie groups and Lie algebras have been completely classified by Élie Cartan. Using the Lie correspondence...