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

TL;DR

This paper explores the connection between geometric configurations, regular subalgebras of E10, and M-theory cosmological solutions, revealing algebraic structures underlying supergravity models.

Contribution

It establishes a link between geometric configurations and rank g regular subalgebras of E10, enriching the algebraic understanding of M-theory cosmology.

Findings

Solutions correspond to rank g regular subalgebras of E10

Dynkin diagrams match incidence diagrams of geometric configurations

Identifies new rank-10 Coxeter subgroups of E10 Weyl group

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}.