On brane solutions related to non-singular kac-moody algebras

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form M = M0 ×M1 × · · · ×Mn, where Mi are Einstein spaces (i _ 1). The sigma-model approach and exact solutions with intersecting composite branes (e.g. solutions with harmonic functions, S-brane and black brane ones) with intersection rules related to non-singular Kac-Moody (KM) algebras (e.g. hyperbolic ones) are reviewed. Some examples of solutions, e.g. corresponding to hyperbolic KM algebras: H2(q, q), AE3, HA2 (1), E10 and Lorentzian KM algebra P10 are presented.