We prove that a two-spherical split Kac-Moody group over a local field naturally provides a topological twin building in the sense of [27]. This existence result and the local-to-global principle for twin building topologies combined with the theory of Moufang foundations as introduced and studied by Mühlherr, Ronan, and Tits allows one to immediately obtain a classification of two-spherical split Moufang topological twin buildings whose underlying Coxeter diagram contains no loop and no isolated vertices.

We prove that a two-spherical split Kac-Moody group over a local field naturally provides a topological twin building in the sense of [26]. This existence result and the local-to-global principle for twin building topologies combined with the theory of Moufang foundations as introduced and studied by Mühlherr, Ronan, and Tits allows one to immediately obtain a classification of two-spherical split Moufang topological twin buildings whose underlying Coxeter diagram contains no loop and no isolated vertices.

No abstract

We use the methods developed in [Pierre-Emmanuel Caprace, "Abstract" homomorphisms of split Kac-Moody groups, Mem. Amer. Math. Soc. 198 (2009); Pierre-Emmanuel Caprace, Bernhard Mühlherr, Isomorphisms of Kac-Moody groups, Invent. Math. 161 (2005) 361-388; Pierre-Emmanuel Caprace, Bernhard Mühlherr, Isomorphisms of Kac-Moody groups which preserve bounded subgroups, Adv. Math. 206 (2006) 250-278] to solve the isomorphism problem of unitary forms of infinite split Kac-Moody groups over finite fields of square order.

No abstract