Generalized Symmetries and Invariant Matter Couplings in Two-dimensional Dilaton Gravity *

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserving transformations only contribute to the dynamics of the dilaton-gravity sector with a reshaping of the dilaton potential. The interaction with matter by means of invariant metrics is also considered. We show in a constructive way that there are metrics which are invariant under two of the symmetries. The most general metrics and minimal couplings that fulfil this condition are found. Work partially supported by the Comisión Interministerial de Ciencia y Tecnoloǵıa and DGICYT. http://www.ugr.es/ m̃navarro; [email protected]