RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 1, Pages 3–24 (Mi izv8766)  

Classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4

N. V. Bogachevabc

a Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
b Lomonosov Moscow State University
c Caucasus Mathematical Center, Adyghe State University, Maikop

Abstract: A hyperbolic lattice is said to be $(1{,}{\kern1pt}2)$-reflective if its automorphism group is generated by $1$- and $2$-reflections up to finite index. We prove that the fundamental polyhedron of a $\mathbb{Q}$-arithmetic cocompact reflection group in three-dimensional Lobachevsky space contains an edge with sufficiently small distance between its framing faces. Using this fact, we obtain a classification of $(1{,}{\kern1pt}2)$-reflective anisotropic hyperbolic lattices of rank $4$.

Keywords: reflective hyperbolic lattices, roots, reflection groups, fundamental polyhedra, Coxeter polyhedra.

Funding Agency Grant Number
Simons Foundation
Partially supported by the Simons Foundation.


DOI: https://doi.org/10.4213/im8766

Full text: PDF file (892 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2019, 83:1, 1–19

Bibliographic databases:

UDC: 519.45+512.7+512.81
MSC: 11H55, 11E12, 20F55, 51F15
Received: 03.02.2018

Citation: N. V. Bogachev, “Classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4”, Izv. RAN. Ser. Mat., 83:1 (2019), 3–24; Izv. Math., 83:1 (2019), 1–19

Citation in format AMSBIB
\Bibitem{Bog19}
\by N.~V.~Bogachev
\paper Classification of (1,2)-reflective anisotropic hyperbolic lattices of rank~4
\jour Izv. RAN. Ser. Mat.
\yr 2019
\vol 83
\issue 1
\pages 3--24
\mathnet{http://mi.mathnet.ru/izv8766}
\crossref{https://doi.org/10.4213/im8766}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019IzMat..83....1B}
\elib{http://elibrary.ru/item.asp?id=37045034}
\transl
\jour Izv. Math.
\yr 2019
\vol 83
\issue 1
\pages 1--19
\crossref{https://doi.org/10.1070/IM8766}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000459866800001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064092454}


Linking options:
  • http://mi.mathnet.ru/eng/izv8766
  • https://doi.org/10.4213/im8766
  • http://mi.mathnet.ru/eng/izv/v83/i1/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
    Number of views:
    This page:124
    References:14
    First page:12

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019