  This paper stands for an application of the noncommutative (NC) Noether
theorem, given in our previous work [AIP Proc 956 (2007) 55-60], for the NC
complex Grosse-Wulkenhaar model. It provides with an extension of a recent work
[Physics Letters B 653 (2007) 343-345]. The local conservation of
energy-momentum tensors (EMTs) is recovered using improvement procedures based
on Moyal algebraic techniques. Broken dilatation symmetry is discussed. NC
gauge currents are also explicitly computed.
