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 $M=M_0\times M_1\times\cdots\times M_n$, where $M_i$ are Einstein spaces ($i\geq1$). 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: $H_2(q,q)$, $AE_3$, $HA_2^{(1)}$, $E_{10}$ and Lorentzian KM algebra $P_{10}$ are presented.