Topological groups of Kac–Moody type, right-angled twinnings and their lattices

Abstract

We construct new groups satisfying the combinatorial axioms of twin root data, by amalgamating spherical parabolic subgroups. The corresponding buildings have right-angled Coxeter groups as Weyl groups. The possibility of mixing several ground fields, not available for Kac–Moody groups, leads to strong non-linearity properties for the groups and some of their subgroups. We also discuss a completion procedure for groups with twin root data which is the starting point for defining a large family of topologically simple groups.