The tangent bundle of an ordinary manifold is a vector bundle whose sheaf of sections? is given by the derivations of the structure sheaf. The same idea applies to a supermanifold to produce a super vector bundle.
The super tangent bundle of a supermanifold is given by the sheaf .
So a super tangent vector is a global section of this sheaf of derivations.
On the supermanifold with its canonical coordinates
there is the odd vector field
whose super Lie bracket with itself vanishes
This odd vector field is left invariant with respect to the super translation group structure on .
This means that is free on one odd generator.