One Class Genera of Lattice Chains Over Number Fields
M. Kirschmer, G. Nebe, in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer International Publishing, Cham, 2018.
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Kirschmer, MarkusLibreCat;
Nebe, Gabriele
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Abstract
We classify all one-class genera of admissible lattice chains of length at least 2 in hermitian spaces over number fields. If L is a lattice in the chain and p the prime ideal dividing the index of the lattices in the chain, then the {p}-arithmetic group Aut(L{p}) acts chamber transitively on the corresponding Bruhat-Tits building. So our classification provides a step forward to a complete classification of these chamber transitive groups which has been announced 1987 (without a detailed proof) by Kantor, Liebler and Tits. In fact we find all their groups over number fields and one additional building with a discrete chamber transitive group.
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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
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Kirschmer M, Nebe G. One Class Genera of Lattice Chains Over Number Fields. In: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer International Publishing; 2018. doi:10.1007/978-3-319-70566-8_22
Kirschmer, M., & Nebe, G. (2018). One Class Genera of Lattice Chains Over Number Fields. In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Springer International Publishing. https://doi.org/10.1007/978-3-319-70566-8_22
@inbook{Kirschmer_Nebe_2018, place={Cham}, title={One Class Genera of Lattice Chains Over Number Fields}, DOI={10.1007/978-3-319-70566-8_22}, booktitle={Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory}, publisher={Springer International Publishing}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2018} }
Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over Number Fields.” In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. Cham: Springer International Publishing, 2018. https://doi.org/10.1007/978-3-319-70566-8_22.
M. Kirschmer and G. Nebe, “One Class Genera of Lattice Chains Over Number Fields,” in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Cham: Springer International Publishing, 2018.
Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over Number Fields.” Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer International Publishing, 2018, doi:10.1007/978-3-319-70566-8_22.
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