R-R Scalars, U-Duality and Solvable Lie Algebras

We consider the group theoretical properties of R-R scalars of string theories in the low-energy supergravity limit and relate them to the solvable Lie subalgebra G_s\subset U of the U-duality algebra that generates the scalar manifold of the theory: exp[G_s]= U/H. Peccei--Quinn symmetries are naturally related with the maximal abelian ideal {\cal A} \subset G_s of the solvable Lie algebra. The solvable algebras of maximal rank occurring in maximal supergravities in diverse dimensions are described in some detail. A particular example of a solvable Lie algebra is a rank one, 2(h_{2,1}+2)-dimensional algebra displayed by the classical quaternionic spaces that are obtained via c-map from the special Kählerian moduli spaces of Calabi-Yau threefolds.