For a morphism of smooth manifolds, the vertical tangent Lie algebroid with respect to is the sub-Lie algebroid of the tangent Lie algebroid of whose Chevalley-Eilenberg algebra is the dg-algebra of horizontal differential forms on with respect to .
For more details on the construction see the examples section at exterior differential systems.
The vertical tangent Lie algebroid is the infinitesimal version of the vertical path ∞-groupoid. It plays a central role in the context of Ehresmann connections and Cartan-Ehresmann ∞-connections.
Created on September 25, 2009 at 17:18:10. See the history of this page for a list of all contributions to it.