One Class Genera of Lattice Chains Over Number Fields

Markus Kirschmer () and Gabriele Nebe ()
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Markus Kirschmer: RWTH Aachen University, Lehrstuhl D für Mathematik
Gabriele Nebe: RWTH Aachen University, Lehrstuhl D für Mathematik

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 503-532 from Springer

Abstract: 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 $$\mathfrak {p} $$ the prime ideal dividing the index of the lattices in the chain, then the { 𝔭 } $$\{ \mathfrak {p} \} $$ -arithmetic group Aut ( L { 𝔭 } ) $$\mathrm {Aut} (L_{ \{ \mathfrak {p} \} }) $$ 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.

Keywords: Genus of lattice; Class number; Affine buildings; Lattice chains; 11E41; 20G30; 20G25 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_22

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DOI: 10.1007/978-3-319-70566-8_22

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