- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:58
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
2
2008
3
Contraction groups in complete Kac–Moody groups
Udo
Baumgartner
University of Wollongong, WOLLONGONG, AUSTRALIA
Jacqui
Ramagge
University of Sydney, SYDNEY, AUSTRALIA
Bertrand
Rémy
Université Claude Bernard Lyon 1, VILLEURBANNE CEDEX, FRANCE
Contraction group, topological Kac–Moody group, totally disconnected, locally compact group
Let G be an abstract Kac–Moody group over a finite field and G 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 G which are not topologically periodic are not closed. (In such groups there always exist elements that are not topologically periodic.)
Topological groups, Lie groups
Group theory and generalizations
General
337
352
10.4171/GGD/43
http://www.ems-ph.org/doi/10.4171/GGD/43