Exact solutions in sigma-model with p-branes

The sigma-model representation in the "p-brane sector" of the multidimensio nal gravitational model with scalar fields and fields of forms is considere d. A subclass of "block-orthogonal" Madjumdar-Papapetrou type solutions rel ated to Lie algebras and governed by a set of harmonic functions is present ed. It is proved that the target space of the sigma-model is a homogeneous space G/H. It is symmetric if and only if the U-vectors governing the sigma -model metric are either coinciding or mutually orthogonal. For nonzero non coinciding U-vectors the Killing equations are solved. Using a block-orthog onal decomposition of the set of the U-vectors it is shown that under rathe r general assumptions the algebra of Killing vectors is a direct sum of sev eral copies of sl(2, R) algebras (corresponding to 1-vector blocks), severa l solvable Lie algebras (corresponding to multivector blocks) and the Killi ng algebra of a flat space. The target space manifold is decomposed in a pr oduct of R-m, several 2-dimensional spaces of constant curvature (e.g. Loba chevsky space, part of de Sitter space) and several solvable Lie group mani folds. Generalization of Freund-Rubin solution to the composite p-brane cas e is also presented.