Marius Sophus Lie (/liː/ LEE; Norwegian: [liː]; 17 December 1842 – 18 February 1899) was a Norwegian mathematician. He largely created the theory of continuous...
17 KB (1,673 words) - 22:09, 27 July 2024
In mathematics, the mathematician Sophus Lie (/liː/ LEE) initiated lines of study involving integration of differential equations, transformation groups...
10 KB (1,257 words) - 23:09, 27 July 2024
In differential geometry, the Lie derivative (/liː/ LEE), named after Sophus Lie by Władysław Ślebodziński, evaluates the change of a tensor field (including...
36 KB (6,849 words) - 00:38, 23 August 2024
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...
2 KB (274 words) - 16:53, 26 April 2024
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...
4 KB (528 words) - 07:44, 29 August 2021
In mathematics, the Lie product formula, named for Sophus Lie (1875), but also widely called the Trotter product formula, named after Hale Trotter, states...
6 KB (712 words) - 06:26, 12 August 2024
has been extended far beyond these origins. Lie groups are named after Norwegian mathematician Sophus Lie (1842–1899), who laid the foundations of the...
64 KB (9,427 words) - 12:29, 18 August 2024
Pseudogroup (redirect from Local Lie group)
concept of a group, originating however from the geometric approach of Sophus Lie to investigate symmetries of differential equations, rather than out of...
12 KB (1,358 words) - 22:02, 18 December 2023
{\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...
61 KB (10,457 words) - 02:56, 14 July 2024
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...
19 KB (2,893 words) - 19:23, 16 August 2023
Élie Cartan (section Lie groups)
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...
28 KB (3,382 words) - 07:54, 21 August 2024
subgroup Arithmetic group Dunkl operator Modular form Langlands program Sophus Lie (1842 – 1899) Wilhelm Killing (1847 – 1923) Élie Cartan (1869 – 1951)...
4 KB (360 words) - 19:55, 10 January 2024
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...
34 KB (2,262 words) - 15:54, 14 May 2024
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)...
28 KB (3,959 words) - 14:56, 19 June 2022
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...
2 KB (252 words) - 05:29, 18 December 2022
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...
28 KB (1,751 words) - 04:02, 10 June 2024
all special functions and all their properties. In fact, Sophus Lie invented the theory of Lie groups when studying the symmetries of differential equations...
10 KB (1,054 words) - 12:38, 11 November 2023
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...
20 KB (2,698 words) - 00:24, 28 March 2024
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...
2 KB (149 words) - 19:26, 20 December 2021
Infinitesimal transformation (category Lie groups)
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...
4 KB (563 words) - 05:38, 17 May 2023
Isaak Moiseevich Yaglom (Russian: Исаа́к Моисе́евич Ягло́м; 6 March 1921 – 17 April 1988) was a Soviet mathematician and author of popular mathematics...
12 KB (1,343 words) - 18:02, 19 August 2024
Versor (section Lie theory)
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...
19 KB (2,804 words) - 22:37, 12 July 2024
Squeeze mapping (section Lie transform)
Ossian Bonnet's (1867) investigations on surfaces of constant curvatures, Sophus Lie (1879) found a way to derive new pseudospherical surfaces from a known...
18 KB (2,494 words) - 02:57, 22 July 2024
One-parameter group (category Lie groups)
One-parameter groups were introduced by Sophus Lie in 1893 to define infinitesimal transformations. According to Lie, an infinitesimal transformation is an...
7 KB (1,003 words) - 23:13, 6 May 2024
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...
3 KB (538 words) - 09:30, 11 October 2023
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...
28 KB (4,308 words) - 17:20, 8 November 2023
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:...
6 KB (720 words) - 12:15, 4 January 2024
Adjoint representation (redirect from Adjoint representation of a Lie algebra)
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...
21 KB (3,516 words) - 07:00, 12 July 2024
Borel subgroup (section Lie algebra)
with positive weight. A Lie subalgebra of g {\displaystyle {\mathfrak {g}}} containing a Borel subalgebra is called a parabolic Lie algebra. Hyperbolic group...
6 KB (948 words) - 19:43, 10 January 2024
complex Lie groups. Real forms of complex semisimple Lie groups and Lie algebras have been completely classified by Élie Cartan. Using the Lie correspondence...
6 KB (818 words) - 14:46, 20 June 2023