A fixed point theorem for Lie groups acting on buildings and applications to Kac-Moody theory

Marquis, Timothée
(2012) Forum mathematicum — Vol. 27, n° 1, p. 449-466 (2015)

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Abstract
We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by simplicial isometries on finite rank buildings with measurable stabilisers of points. As an application, we deduce amongst other things that all topological one-parameter subgroups of a real or complex Kac-Moody group are obtained by exponentiating ad-locally finite elements of the corresponding Lie algebra.
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Marquis, T. (2012). A fixed point theorem for Lie groups acting on buildings and applications to Kac-Moody theory. Forum mathematicum, 27(1), 449-466. https://doi.org/10.1515/forum-2012-0111 (Original work published 2015)