Carnot group
id:
carnot-group-319-14942669
title:
Carnot group
text:
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. The subbundle of the tangent bundle associated to this eigenspace is called horizontal. On a Carnot group, any norm on the horizontal subbundle gives rise to a Carnot–Carathéodory metric. Carnot–Carathéodory metrics have metric dilations; they are asymptotic cones of finitely-generated nilpotent groups, and of
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wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Carnot_group
date created:
date modified:
2023-04-04T09:39:04Z
main entity:
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image:
fields total:
13
integrity:
13