In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses...
64 KB (9,479 words) - 09:21, 13 September 2024
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 be...
34 KB (2,262 words) - 15:54, 14 May 2024
In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for...
27 KB (4,458 words) - 00:15, 27 July 2024
table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness;...
14 KB (363 words) - 12:53, 8 April 2024
algebras are closely related to Lie groups, which are groups that are also smooth manifolds: every Lie group gives rise to a Lie algebra, which is the tangent...
61 KB (10,457 words) - 07:08, 29 August 2024
mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points...
22 KB (2,985 words) - 10:42, 28 March 2023
differential geometry, a Lie group action is a group action adapted to the smooth setting: G {\displaystyle G} is a Lie group, M {\displaystyle M} is a...
8 KB (1,333 words) - 16:47, 18 August 2024
In geometry, an abelian Lie group is a Lie group that is an abelian group. A connected abelian real Lie group is isomorphic to R k × ( S 1 ) h {\displaystyle...
2 KB (213 words) - 13:43, 3 September 2021
universal complexification of a real Lie group is given by a continuous homomorphism of the group into a complex Lie group with the universal property that...
52 KB (7,216 words) - 14:30, 2 December 2022
In mathematics, Lie group decompositions are used to analyse the structure of Lie groups and associated objects, by showing how they are built up out of...
3 KB (346 words) - 19:47, 22 May 2024