SOLVABLE LIE-ALGEBRAS IN TYPE IIA, TYPE IIB AND M-THEORIES

We study some applications of solvable Lie algebras in type IIA, type IIB and M-theories. RR and NS generators find a natural geometric inte rpretation in this framework. Special emphasis is given to the countin g of the abelian nilpotent ideals (translational symmetries of the sca lar manifolds) in arbitrary D dimensions. These are seen to be related , using Dynkin diagram techniques, to one-form counting in D + 1 dimen sions. A recipe for gauging isometries in this framework is also prese nted. In particular, we list the gauge groups both for compact and tra nslational isometries. The former agree with some results already exis ting in gauged supergravity. The latter should be possibly related to the study of partial supersymmetry breaking, as suggested by a similar role played by solvable Lie algebras in N = 2 gauged supergravity. (C ) 1997 Elsevier Science B.V.