Symmetries of the stationary Einstein - Maxwell-dilaton system

The gravity-coupled three-dimensional -model describing the stationary Einstein - Maxwell-dilaton system with a general dilaton coupling constant is studied. The Killing equations for the corresponding five-dimensional target space are solved explicitly. It is shown that for the symmetry algebra is isomorphic to the maximal solvable subalgebra of the sl(3,R). For two critical values and , the Killing algebra is enlarged to the full sl(3,R) and the corresponding to the five-dimensional Kaluza - Klein and the four-dimensional Brans - Dicke - Maxwell theories, respectively. These two models are examined in terms of the same real variables. Non-trivial discrete maps between subspaces of the target space are found and used to generate new arbitrary- solutions to the dilaton gravity.