Geometric Configurations, Regular Subalgebras of E10 and M-Theory Cosmology

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 $g$ 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}.

arXiv comment48 pages, 27 figures, 5 tables, references added, typos corrected

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Cited by in corpus (10)

• String Cosmology: A Review
• Spacelike Singularities and Hidden Symmetries of Gravity
• Finsler Black Holes Induced by Noncommutative Anholonomic Distributions in Einstein Gravity
• Arithmetic and Hyperbolic Structures in String Theory
• Borcherds Algebras and N=4 Topological Amplitudes
• Some Algebraic Aspects of Half-BPS Bound States in M-Theory
• A Special Class of Rank 10 and 11 Coxeter Groups
• Deformations of Cosmological Solutions of D=11 Supergravity
• On Brane Solutions Related to Non-Singular Kac-Moody Algebras
• $\pi$-systems and the embedding problem for rank $2$ Kac-Moody Lie algebras