We obtain global analytic hypoellipticity for a class of differential operators that can be expressed as \(P = \sum _{j=1}^\nu X_j^2 + X_0 + a\) with real-analytic coefficients on compact Lie groups such that the vector fields satisfy Hörmander’s finite type condition; there exists a closed subgroup whose action leaves the vector fields invariant; and the operator must be elliptic in directions transversal to the action of the subgroup. This paves the way for further studies on the regularity of sums of squares on principal fiber bundles.
