On Symmetries of Target Space for Sigma-model of p -brane Origin

The target space M for the sigma-model appearing in theories with p-branes is considered. It is proved that M 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 noncoinciding U -vectors the Killing equations are solved. Using a block-orthogonal decomposition of the set of the U -vectors it is shown that under rather general assumptions the algebra of Killing vectors is a direct sum of several copies of sl(2,R) algebras (corresponding to 1-vector blocks), several solvable Lie algebras (corresponding to multivector blocks) and the Killing algebra of a flat space. The target space manifold is decomposed in a product of R m , several 2-dimensional spaces of constant curvature (e.g. Lobachevsky space, part of anti-de Sitter space) and several solvable Lie group manifolds.