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research article
A lattice in more than two Kac–Moody groups is arithmetic
Let Gamma be an irreducible lattice in a product of n infinite irreducible complete Kac–Moody groups of simply laced type over finite fields. We show that if n>2, then each Kac–Moody groups is in fact a simple algebraic group over a local field and Gamma is an arithmetic lattice. This relies on the following alternative which is satisfied by any irreducible lattice provided n>1: either Gamma is an S-arithmetic (hence linear) group, or it is not residually finite. In that case, it is even virtually simple when the ground field is large enough. More general CAT(0) groups are also considered throughout.
Type
research article
Web of Science ID
WOS:000307305300020
Authors
Publication date
2012
Published in
Volume
190
Issue
1
Start page
413
End page
444
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
December 6, 2008
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