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...

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...

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...

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...

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...

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

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...

is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for...

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...

\operatorname {GL} (n,\mathbb {R} )} over the field of real numbers is a real Lie group of dimension n 2 {\displaystyle n^{2}} . To see this, note that the set...

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...

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...

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

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...

influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become...

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...

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...

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...

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...

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...

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...

group H3(R). It is a nilpotent real Lie group of dimension 3. In addition to the representation as real 3×3 matrices, the continuous Heisenberg group...

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

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,...

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...

Lie group of n × n rotation matrices, SO(n), is not simply connected, so Lie theory tells us it is a homomorphic image of a universal covering group....

In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any...

general group. Lie groups appear in symmetry groups in geometry, and also in the Standard Model of particle physics. The Poincaré group is a Lie group consisting...

A lie is an assertion that is believed to be false, typically used with the purpose of deceiving or misleading someone. The practice of communicating...