Vol. 13, No. 1, 2013

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On topological split Kac-Moody groups and their twin buildings

Tobias Hartnick, Ralf Köhl and Andreas Mars

Vol. 13 (2013), No. 1, 1–71

We prove that a two-spherical split Kac–Moody group over a local field naturally provides a topological twin building in the sense of Kramer. 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 obtain a similar classification for split Moufang topological twin buildings.

Received: 24 January 2011
Accepted: 3 October 2013
Tobias Hartnick
Mathematics Department
32000 Haifa
Ralf Köhl
Andreas Mars