Abstract
We prove a simplicity criterion for certain twin tree lattices. It applies to all rank-2 Kac–Moody groups over finite fields with non-trivial commutation relations, thereby yielding examples of simple non-uniform lattices in the product of two trees.
P.-E. Caprace—F.R.S.-FNRS Research Associate, supported in part by FNRS grant F.4520.11 and the European Research Council
B. Rémy—Supported in part by Institut Mittag-Leffler and by the GDSous/GSG project (ANR-12-BS01-0003).
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Acknowledgments
The second author warmly thanks the organizers of the Special Quarter Topology and Geometric Group Theory held at the Ohio State University (Spring 2011). We are grateful to Bernhard Mühlherr for pointing out the degeneracy of the commutation relations when the defining characteristic divides m in Theorem 5.1.2.
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Caprace, PE., Rémy, B. (2016). Simplicity of Twin Tree Lattices with Non-trivial Commutation Relations. In: Davis, M., Fowler, J., Lafont, JF., Leary, I. (eds) Topology and Geometric Group Theory. Springer Proceedings in Mathematics & Statistics, vol 184. Springer, Cham. https://doi.org/10.1007/978-3-319-43674-6_5
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DOI: https://doi.org/10.1007/978-3-319-43674-6_5
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