In mathematics, a Lie group (pronounced /liː/ LEE) is a group that is also a differentiable manifold, such that group multiplication and taking inverses...

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...

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...

table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness;...

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...

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...

a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of...

of Lie group topics, by Wikipedia page. See Table of Lie groups for a list General linear group, special linear group SL2(R) SL2(C) Unitary group, special...

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...

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...

defined as the unit group of the matrix ring M(n, R). The general linear group GL(n, R) over the field of real numbers is a real Lie group of dimension n2...

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...

Lie groups form a class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups...

In mathematics, a Poisson–Lie group is a Poisson manifold that is also a Lie group, with the group multiplication being compatible with the Poisson algebra...

include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in...

Cartan. The foundation of Lie theory is the exponential map relating Lie algebras to Lie groups which is called the Lie group–Lie algebra correspondence...

equals its transpose). The orthogonal group is an algebraic group and a Lie group. It is compact. The orthogonal group in dimension n has two connected components...

matrices which represent the groups. In Cartan's classification of the simple Lie algebras, the Lie algebra of the complex group Sp(2n, C) is denoted Cn,...

non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics. The Poincaré group consists of...

unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group may...

representation of a Lie group. Roughly speaking, the representations of Lie algebras are the differentiated form of representations of Lie groups, while the representations...

isomorphism) only one connected compact Lie group having Lie algebra of type G 2 {\displaystyle G_{2}} ; this group is simply connected and has trivial center...

the correspondence between Lie groups and Lie algebras, Lie groupoids are the global counterparts of Lie algebroids. Lie groupoids were introduced by...

A Lie group integrator is a numerical integration method for differential equations built from coordinate-independent operations such as Lie group actions...

Lie to Me (stylized as Lie to me*) is an American crime drama television series created by Samuel Baum that aired on Fox from January 21, 2009, to January...

geometry, a complex Lie group is a Lie group over the complex numbers; i.e., it is a complex-analytic manifold that is also a group in such a way G × G...

way to structure a given group as a supergroup. A supergroup is like a Lie group in that there is a well defined notion of smooth function defined on them...

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...

particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system...

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...