On Brane Solutions Related to Non-Singular Kac-Moody Algebras

Abstract

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 ($i\ge 1$). 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: $H_2(q,q)$, $A{E}_3$, $H{A}_2^{(1)}$, $E_{10}$ and Lorentzian KM algebra $P_{10}$ are presented.

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• On billiard approach in multidimensional cosmological models