(2$+$1)-dimensional gravity from Maxwell and semisimple extension of the Poincaré gauge symmetric models

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.