A note on noncommutative Chern-Simons theories

The three-dimensional Chern-Simons theory on R-theta(2) x R is studied. Con sidering the gauge transformations under the group elements which are going to one at infinity, we show that under arbitrary (finite) gauge transforma tions action changes with an integer multiple of 2 pi if,the level of nonco mmutative Chern-Simons is quantized. We also briefly discuss the case of th e noncommutative torus and some other possible extensions. (C) 2001 Publish ed by Elsevier Science B.V.