{"title":"One Class Genera of Lattice Chains Over Number Fields","publication":"Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory","extern":"1","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."}],"language":[{"iso":"eng"}],"place":"Cham","date_updated":"2023-04-04T09:08:19Z","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>","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.","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>.","short":"M. Kirschmer, G. Nebe, in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer International Publishing, Cham, 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>."},"publisher":"Springer International Publishing","type":"book_chapter","department":[{"_id":"102"}],"_id":"42788","status":"public","doi":"10.1007/978-3-319-70566-8_22","date_created":"2023-03-07T08:23:48Z","publication_status":"published","author":[{"id":"82258","first_name":"Markus","full_name":"Kirschmer, Markus","last_name":"Kirschmer"},{"first_name":"Gabriele","full_name":"Nebe, Gabriele","last_name":"Nebe"}],"year":"2018","user_id":"93826","publication_identifier":{"isbn":["9783319705651","9783319705668"]}}