Carnot group
Encyclopedia
In mathematics, a Carnot group is a simply connected nilpotent Lie group
, together with a derivation of its Lie algebra
such that the subspace with eigenvalue 1 generates the Lie algebra. Carnot groups have a Carnot–Carathéodory metric. They were introduced by and .
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
, together with a derivation of its Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
such that the subspace with eigenvalue 1 generates the Lie algebra. Carnot groups have a Carnot–Carathéodory metric. They were introduced by and .