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arXiv · 0706.2713

Contraction groups in complete Kac-Moody groups

Udo Baumgartner·Jacqui Ramagge·Bertrand Remy
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Abstract

Let $G$ be an abstract Kac-Moody group over a finite field and $\bar{G}$ be the closure of the image of $G$ in the automorphism group of its positive building. We show that if the Dynkin diagram associated to $G$ is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in $\bar{G}$ which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

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Udo Baumgartner, Jacqui Ramagge, Bertrand Remy. 2007-06-19. Contraction groups in complete Kac-Moody groups. https://doi.org/10.4171/ggd/43

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