Area preserving diffeomorphisms and Yang-Mills theory in two   noncommutative dimensions
  We present some evidence that noncommutative Yang-Mills theory in two dimensions is not invariant under area preserving diffeomorphisms, at variance with the commutative case. Still, invariance under linear unimodular maps survives, as is proven by means of a fairly general argument. 
A. Bassetto, G. De Pol, A. Torrielli and F. Vian