This ticket adds Lie bracket to vector fields, giving the structure of Lie algebroid to the set X(M) of all vector fields over the manifold M.

Depends on #19092
Depends on #20770

CC: @egourgoulhon

Component: geometry

Keywords: lie algebras, days74

Author: Travis Scrimshaw

Branch/Commit: 2f1d037

Reviewer: Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/20771