On a class of automorphisms in <b>H</b> ² which resemble the property of preserving volume

We give a possible extension of definition shears and overshears in the case two non commutative (quaternionic) variables relation with associated vector fields flows. define divergence operator determine divergence. Given non-existence quaternionic volume form on H2, we automorphisms to be time-one maps preserving 0. To these classes Andersen–Lempert theory applies. Finally, exhibit an example automorphism, which is not closure set finite compositions even though its restriction complex subspace C × shears.