Noncommutative Lorentz Symmetry & the Seiberg-Witten Map

In commutative gauge theory one finds two representations of the conformal transformations, a `primitive' and a `covariant' related to the canonical and the symmetrical energy-momentum tensor, respectively. In noncommutative Yang-Mills theory one finds the same two representation provided one also transforms the noncommutative tensor theta. We find a surprising relation between covariant coordinates, the Seiberg-Witten map and the noncommutative, covariant representation of the (rigid) conformal transformations.