Innovations in Incidence Geometry

On topological split Kac-Moody groups and their twin buildings

Tobias Hartnick, Ralf Köhl, and Andreas Mars

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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.

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Innov. Incidence Geom., Volume 13, Number 1 (2013), 1-71.

Received: 24 January 2011
Accepted: 3 October 2013
First available in Project Euclid: 28 February 2019

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Hartnick, Tobias; Köhl, Ralf; Mars, Andreas. On topological split Kac-Moody groups and their twin buildings. Innov. Incidence Geom. 13 (2013), no. 1, 1--71. doi:10.2140/iig.2013.13.1.

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