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...

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

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...

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...

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...

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...

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...