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Mosc. Math. J., 2015, Volume 15, Number 3, Pages 593–602 (Mi mmj575)  

This article is cited in 5 scientific papers (total in 5 papers)

Non-arithmetic hyperbolic reflection groups in higher dimensions

E. B. Vinberg

Department of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991, Russian Federation

Abstract: We construct examples of non-arithmetic (non-cocompact) cofinite discrete reflection groups in $n$-dimensional Lobachevsky spaces $L^n$ for all $n\leq12$ and for $n=14,18$.

Key words and phrases: Lobachevsky (hyperbolic) space, discrete group, reflection group, arithmetic group.

DOI: https://doi.org/10.17323/1609-4514-2015-15-3-593-602

Full text: http://www.mathjournals.org/.../2015-015-003-008.html
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Bibliographic databases:

MSC: 51F15, 22E40
Received: October 16, 2014
Language:

Citation: E. B. Vinberg, “Non-arithmetic hyperbolic reflection groups in higher dimensions”, Mosc. Math. J., 15:3 (2015), 593–602

Citation in format AMSBIB
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\by E.~B.~Vinberg
\paper Non-arithmetic hyperbolic reflection groups in higher dimensions
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 3
\pages 593--602
\mathnet{http://mi.mathnet.ru/mmj575}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-3-593-602}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3427439}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000365392600008}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. Guglielmetti, “CoxIter—computing invariants of hyperbolic Coxeter groups”, LMS J. Comput. Math., 18:1 (2015), 754–773  crossref  mathscinet  zmath  isi  elib  scopus
    2. R. Guglielmetti, M. Jacquemet, R. Kellerhals, “On commensurable hyperbolic Coxeter groups”, Geom. Dedicata, 183:1 (2016), 143–167  crossref  mathscinet  zmath  isi  scopus
    3. M. Belolipetsky, “Arithmetic hyperbolic reflection groups”, Bull. Amer. Math. Soc. (N.S.), 53:3 (2016), 437–475  crossref  mathscinet  zmath  isi  scopus
    4. V. Emery, “On volumes of quasi-arithmetic hyperbolic lattices”, Sel. Math.-New Ser., 23:4 (2017), 2849–2862  crossref  mathscinet  zmath  isi  scopus
    5. R. Kellerhals, “On minimal covolume hyperbolic lattices”, 5, no. 3, 2017, 43  crossref  zmath  isi  scopus
  • Moscow Mathematical Journal
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