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

• Autores: Bertrand Rémy, Mark Ronan
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 81, Nº 1, 2006, págs. 191-219
• Idioma: inglés
• DOI: 10.4171/cmh/49
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• Resumen

  • 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.