What are the Bounds on Space-Time Noncommutativity?
  In this article we consider the bounds on the noncommutative nature of space-time. We argue that these bounds are extremely model dependent. In the only phenomenologically viable framework, i.e. when the fields are taken to be in the enveloping of the Lie algebra, the constraints are fairly loose and only of the order of a few TeV. 
Xavier Calmet