nLab
vertical tangent Lie algebroid

For π:YX\pi : Y \to X a morphism of smooth manifolds, the vertical tangent Lie algebroid with respect to π\pi is the sub-Lie algebroid T vertYTXT_{vert} Y \hookrightarrow T X of the tangent Lie algebroid TYT Y of YY whose Chevalley-Eilenberg algebra is the dg-algebra of horizontal differential forms on YY with respect to π\pi.

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 17:34:22 by Urs Schreiber (88.128.81.237)