---
_id: '42788'
abstract:
- lang: eng
  text: 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.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: Gabriele
  full_name: Nebe, Gabriele
  last_name: Nebe
citation:
  ama: 'Kirschmer M, Nebe G. One Class Genera of Lattice Chains Over Number Fields.
    In: <i>Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory</i>.
    Springer International Publishing; 2018. doi:<a href="https://doi.org/10.1007/978-3-319-70566-8_22">10.1007/978-3-319-70566-8_22</a>'
  apa: Kirschmer, M., &#38; Nebe, G. (2018). One Class Genera of Lattice Chains Over
    Number Fields. In <i>Algorithmic and Experimental Methods in Algebra, Geometry,
    and Number Theory</i>. Springer International Publishing. <a href="https://doi.org/10.1007/978-3-319-70566-8_22">https://doi.org/10.1007/978-3-319-70566-8_22</a>
  bibtex: '@inbook{Kirschmer_Nebe_2018, place={Cham}, title={One Class Genera of Lattice
    Chains Over Number Fields}, DOI={<a href="https://doi.org/10.1007/978-3-319-70566-8_22">10.1007/978-3-319-70566-8_22</a>},
    booktitle={Algorithmic and Experimental Methods in Algebra, Geometry, and Number
    Theory}, publisher={Springer International Publishing}, author={Kirschmer, Markus
    and Nebe, Gabriele}, year={2018} }'
  chicago: 'Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains
    Over Number Fields.” In <i>Algorithmic and Experimental Methods in Algebra, Geometry,
    and Number Theory</i>. Cham: Springer International Publishing, 2018. <a href="https://doi.org/10.1007/978-3-319-70566-8_22">https://doi.org/10.1007/978-3-319-70566-8_22</a>.'
  ieee: 'M. Kirschmer and G. Nebe, “One Class Genera of Lattice Chains Over Number
    Fields,” in <i>Algorithmic and Experimental Methods in Algebra, Geometry, and
    Number Theory</i>, Cham: Springer International Publishing, 2018.'
  mla: Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over
    Number Fields.” <i>Algorithmic and Experimental Methods in Algebra, Geometry,
    and Number Theory</i>, Springer International Publishing, 2018, doi:<a href="https://doi.org/10.1007/978-3-319-70566-8_22">10.1007/978-3-319-70566-8_22</a>.
  short: 'M. Kirschmer, G. Nebe, in: Algorithmic and Experimental Methods in Algebra,
    Geometry, and Number Theory, Springer International Publishing, Cham, 2018.'
date_created: 2023-03-07T08:23:48Z
date_updated: 2023-04-04T09:08:19Z
department:
- _id: '102'
doi: 10.1007/978-3-319-70566-8_22
extern: '1'
language:
- iso: eng
place: Cham
publication: Algorithmic and Experimental Methods in Algebra, Geometry, and Number
  Theory
publication_identifier:
  isbn:
  - '9783319705651'
  - '9783319705668'
publication_status: published
publisher: Springer International Publishing
status: public
title: One Class Genera of Lattice Chains Over Number Fields
type: book_chapter
user_id: '93826'
year: '2018'
...