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 of 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 A subset of 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 the c-map from the special Kahlerian moduli spaces of Calabi-Yau threefolds. (C) 1997 Published by Elsevier Science B.V.