  We obtain 2 + 1 dimensional gravity with cosmological constant which is
coupled to gauge fields, using Maxwell and semi-simple extension of the
Poincare gauge symmetric models (i.e. Chern-Simons models with these gauge
groups). Also, we obtain some Ads and BTZ type solutions for the classical
equations of motion for these 2 + 1 dimensional gravities. For the semi-simple
extension of the Poincare gauge group we investigate the Ads/CFT correspondence
and show that the model at the boundary is equivalent to the sum of three WZW
models over group SO(2,1). Then, we show that the central charge of the CFT is
the same as that of CFT at the boundary of Ads spacetime related to the
Chern-Simons model with gauge group SO(2,2). Finally, we show that these two 2
+ 1 dimensional gravity models are dual (canonically transformed) to each
other.
