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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 ($i geq 1$). 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: $H_2(q,q)$, $AE_3$, $HA_2^{(1)}$, $E_{10}$ and Lorentzian KM algebra $P_{10}$ are presented.
We show that an $SL(2,R)_L times SL(2,R)_R$ Chern-Simons theory coupled to a source on a manifold with the topology of a disk correctly describes the entropy of the AdS$_3$ black hole. The resulting boundary WZNW theory leads to two copies of a twist
We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilize
We describe Hom-Lie structures on affine Kac-Moody and related Lie algebras, and discuss the question when they form a Jordan algebra.
The motion of a dynamical system on an $n$-dimensional configuration space may be regarded as the lightlike shadow of null geodsics moving in an $(n+2)$ dimensional spacetime known as its Einsenhart-Duval lift. In this paper it is shown that if the c
We determine commutative post-Lie algebra structures on some infinite-dimensional Lie algebras. We show that all commutative post-Lie algebra structures on loop algebras are trivial. This extends the results for finite-dimensional perfect Lie algebra