Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology
arXiv:hep-th/0606123 · doi:10.1088/1126-6708/2006/10/021
Abstract
We re-examine previously found cosmological solutions to eleven-dimensional supergravity in the light of the E_{10}-approach to M-theory. We focus on the solutions with non zero electric field determined by geometric configurations (n_m, g_3), n\leq 10. We show that these solutions are associated with rank regular subalgebras of E_{10}, the Dynkin diagrams of which are the (line) incidence diagrams of the geometric configurations. Our analysis provides as a byproduct an interesting class of rank-10 Coxeter subgroups of the Weyl group of E_{10}.
48 pages, 27 figures, 5 tables, references added, typos corrected