Abstract
We establish an arithmeticity vs. nonlinearity alternative for irreducible lattices in suitable product groups, for instance products of topologically simple groups. This applies notably to a (large class of) Kac–Moody groups. The alternative relies heavily on the superrigidity theorem we propose since we follow Margulis’ reduction of arithmeticity to superrigidity.
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Monod N. (2005). Superrigidity for irreducible lattices and geometric splitting, C.R. Acad. Sci. Paris. Ser. I
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Mathematics Subject Classiffications (2000). 22E40, 22E50, 53C24, 20G15
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Monod, N. Arithmeticity vs. Nonlinearity for Irreducible Lattices. Geom Dedicata 112, 225–237 (2005). https://doi.org/10.1007/s10711-004-6162-9
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DOI: https://doi.org/10.1007/s10711-004-6162-9