Contraction groups in complete Kac-Moody groups

Details Contraction groups in complete Kac-Moody groups Contraction groups in complete Kac-Moody groups

2007-06-19

arxiv.org/abs/0706.2713v1

Mathematics

Group Theory

Scientific paper

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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