Global hypoellipticity and global solvability for a model of differential operators of the type sums of squares

Let M be a compact, connected smooth manifold and G a compact, connected Lie group. We will discuss global hypoellipticity and global solvability for a model of operators on M × G that is defined as a sum of squares of vector fields in M and G and is also invariant under the left action of G. This a joint work with Gabriel Araújo (University of São Paulo), Igor A. Ferra (Federal University of São Carlos).