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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Uspekhi Mat. Nauk, 1985, Volume 40, Issue 1(241), Pages 29–66 (Mi umn2140)  

This article is cited in 47 scientific papers (total in 49 papers)

Hyperbolic reflection groups

È. B. Vinberg


Full text: PDF file (5241 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1985, 40:1, 31–75

Bibliographic databases:

UDC: 513.77+519.45
MSC: 51F15, 20F55, 51M20, 52Bxx
Received: 06.01.1983

Citation: È. B. Vinberg, “Hyperbolic reflection groups”, Uspekhi Mat. Nauk, 40:1(241) (1985), 29–66; Russian Math. Surveys, 40:1 (1985), 31–75

Citation in format AMSBIB
\Bibitem{Vin85}
\by \`E.~B.~Vinberg
\paper Hyperbolic reflection groups
\jour Uspekhi Mat. Nauk
\yr 1985
\vol 40
\issue 1(241)
\pages 29--66
\mathnet{http://mi.mathnet.ru/umn2140}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=783604}
\zmath{https://zbmath.org/?q=an:0579.51015}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1985RuMaS..40...31V}
\transl
\jour Russian Math. Surveys
\yr 1985
\vol 40
\issue 1
\pages 31--75
\crossref{https://doi.org/10.1070/RM1985v040n01ABEH003527}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1985AWR2400002}


Linking options:
  • http://mi.mathnet.ru/eng/umn2140
  • http://mi.mathnet.ru/eng/umn/v40/i1/p29

    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

    This publication is cited in the following articles:
    1. I. Ya. Aref'eva, I. V. Volovich, “Manifolds of constant negative curvature as vacuum solutions in Kaluza–Klein and superstring theories”, Theoret. and Math. Phys., 64:2 (1985), 866–871  mathnet  crossref  mathscinet  zmath  isi
    2. I. Ya. Aref'eva, I. V. Volovich, B. G. Dragovich, “Spontaneous reduction in multidimensional ($D=10, 11$) supergravity theories with arbitrary signature”, Theoret. and Math. Phys., 70:3 (1987), 297–304  mathnet  crossref  mathscinet  isi
    3. S. V. Matveev, A. T. Fomenko, “Constant energy surfaces of Hamiltonian systems, enumeration of three-dimensional manifolds in increasing order of complexity, and computation of volumes of closed hyperbolic manifolds”, Russian Math. Surveys, 43:1 (1988), 3–24  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities. II”, Math. USSR-Izv., 33:2 (1989), 355–372  mathnet  crossref  mathscinet  zmath
    5. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248  mathnet  crossref  mathscinet  zmath  isi
    6. Ruth Kellerhals, “On Schläfli's reduction formula”, Math Z, 206:1 (1991), 193  crossref  mathscinet  zmath  isi
    7. O. V. Schwarzman, “On Fuchsian Groups of Genus Zero”, Funct. Anal. Appl., 28:4 (1994), 276–281  mathnet  crossref  mathscinet  zmath  isi
    8. R. Kellerhals, “Volumes in hyperbolic 5-space”, GAFA Geom funct anal, 5:4 (1995), 640  crossref  mathscinet  zmath  isi
    9. Ruth Kellerhals, “Shape and size through hyperbolic eyes”, Math Intelligencer, 17:2 (1995), 21  crossref  mathscinet  zmath  isi
    10. J. J. Seidel, “Geometric representations of graphs”, Linear and Multilinear Algebra, 39:1-2 (1995), 45  crossref
    11. G.J Heckman, “The volume of hyperbolic Coxeter polytopes of even dimension”, Indagationes Mathematicae, 6:2 (1995), 189  crossref
    12. Frank Esselmann, “The classification of compact hyperbolic Coxeterd-polytopes withd+2 facets”, Comment Math Helv, 71:1 (1996), 229  crossref  mathscinet  zmath  isi
    13. V. V. Nikulin, “Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac–Moody algebras”, Izv. Math., 60:2 (1996), 305–334  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. D. V. Alekseevskii, V. O. Bugaenko, G. I. Olshanskii, V. L. Popov, O. V. Schwarzman, “Érnest Borisovich Vinberg (on his 60th birthday)”, Russian Math. Surveys, 52:6 (1997), 1335–1343  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. Luisa Paoluzzi, “Psl(2,q) quotients of some hyperbolic tetrahedral and Coxeter groups”, Communications in Algebra, 26:3 (1998), 759  crossref
    16. V. V. Nikulin, “On the Classification of Hyperbolic Root Systems of Rank Three”, Proc. Steklov Inst. Math., 230:3 (2000), 1–241  mathnet  mathscinet  zmath
    17. V. A. Gritsenko, V. V. Nikulin, “On classification of Lorentzian Kac–Moody algebras”, Russian Math. Surveys, 57:5 (2002), 921–979  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. Leung N. Reiner V., “The Signature of a Toric Variety”, Duke Math. J., 111:2 (2002), 253–286  isi
    19. V. O. Bugaenko, “Klassifikatsiya mnogogrannikov Kokstera”, Matem. prosv., ser. 3, 7, MTsNMO, M., 2003, 82–106  mathnet
    20. P. V. Tumarkin, “Hyperbolic $n$-dimensional Coxeter polytopes with $n+3$ facets”, Russian Math. Surveys, 58:4 (2003), 805–806  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    21. Michel Deza, Mathieu Dutour, Mikhail Shtogrin, “On simplicial and cubical complexes with short links”, Isr J Math, 144:1 (2004), 109  crossref  mathscinet  zmath  isi  elib
    22. P. V. Tumarkin, “Hyperbolic Coxeter $N$-Polytopes with $n+2$ Facets”, Math. Notes, 75:6 (2004), 848–854  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. E. Ya. Klimenko, N. V. Kopteva, “Discrete $\mathscr{RP}$-groups with a parabolic generator”, Siberian Math. J., 46:6 (2005), 1069–1076  mathnet  crossref  mathscinet  zmath  isi
    24. Dmitri V. Alekseevsky, Andreas Kriegl, Mark Losik, Peter W. Michor, “Reflection groups on Riemannian manifolds”, Annali di Matematica, 186:1 (2007), 25  crossref  mathscinet  isi  elib
    25. A Felikson, P Tumarkin, T Zehrt, “On hyperbolic Coxeter n-polytopes with n + 2 facets”, advg, 7:2 (2007), 177  crossref  mathscinet  zmath  isi  elib
    26. P. V. Tumarkin, A. A. Felikson, “On simple ideal hyperbolic Coxeter polytopes”, Izv. Math., 72:1 (2008), 113–126  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    27. Dolgachev, IV, “Reflection groups in algebraic geometry”, Bulletin of the American Mathematical Society, 45:1 (2008), 1  crossref  mathscinet  zmath  isi
    28. Anna Felikson, Pavel Tumarkin, “On hyperbolic Coxeter polytopes with mutually intersecting facets”, Journal of Combinatorial Theory, Series A, 115:1 (2008), 121  crossref
    29. Brent Everitt, Robert B. Howlett, “Weyl groups, lattices and geometric manifolds”, Geom Dedicata, 2009  crossref  mathscinet  isi
    30. O. V. Schwarzman, “Hyperbolic Chevalley Groups on $\mathbb{C}^2$”, Funct. Anal. Appl., 43:2 (2009), 132–139  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    31. S. Finashin, V. Kharlamov, “On the deformation chirality of real cubic fourfolds”, Compositio Math, 145:5 (2009), 1277  crossref  mathscinet  zmath  isi
    32. Anna Felikson, Pavel Tumarkin, “Coxeter polytopes with a unique pair of non-intersecting facets”, Journal of Combinatorial Theory, Series A, 116:4 (2009), 875  crossref
    33. Nikulin V.V., “On Ground Fields of Arithmetic Hyperbolic Reflection Groups”, Groups and Symmetries: From Neolithic Scots To John McKay, Crm Proceedings & Lecture Notes, 47, 2009, 299–326  isi
    34. Ma. Louise Antonette N. De Las Peñas, Rene P. Felix, Glenn R. Laigo, “On subgroups of hyperbolic tetrahedral Coxeter groups”, Zeitschrift für Kristallographie, 225:8 (2010), 313  crossref
    35. V. V. Nikulin, “The transition constant for arithmetic hyperbolic reflection groups”, Izv. Math., 75:5 (2011), 971–1005  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    36. Alexander Kolpakov, “Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers”, European Journal of Combinatorics, 33:8 (2012), 1709  crossref
    37. D. Panov, A. Petrunin, “Telescopic actions”, Geom. Funct. Anal, 2012  crossref
    38. Anna Felikson, Pavel Tumarkin, “Essential hyperbolic Coxeter polytopes”, Isr. J. Math, 2013  crossref
    39. V.V.. Nikulin, “Elliptic Fibrations On K3 Surfaces”, Proceedings of the Edinburgh Mathematical Society, 2013, 1  crossref
    40. Belolipetsky M. Mcleod J., “Reflective and Quasi-Reflective Bianchi Groups”, Transform. Groups, 18:4 (2013), 971–994  crossref  isi
    41. John Mcleod, “Hyperbolic Coxeter Pyramids”, APM, 03:01 (2013), 78  crossref
    42. Anna Felikson, Jessica Fintzen, Pavel Tumarkin, “Reflection subgroups of odd-angled Coxeter groups”, Journal of Combinatorial Theory, Series A, 126 (2014), 92  crossref
    43. Matthieu Jacquemet, “The Inradius of a Hyperbolic Truncated
      $$n$$
      n -Simplex”, Discrete Comput Geom, 2014  crossref
    44. Belolipetsky M., “Arithmetic hyperbolic reflection groups”, Bull. Amer. Math. Soc., 53:3 (2016), 437–475  crossref  mathscinet  zmath  isi  elib  scopus
    45. A. Yu. Vesnin, “Right-angled polyhedra and hyperbolic 3-manifolds”, Russian Math. Surveys, 72:2 (2017), 335–374  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    46. Gritsenko V. Nikulin V.V., “Lorentzian Kac-Moody Algebras With Weyl Groups of 2-Reflections”, Proc. London Math. Soc., 116:3 (2018), 485–533  crossref  isi
    47. N. V. Bogachev, A. Yu. Perepechko, “Vinberg's Algorithm for Hyperbolic Lattices”, Math. Notes, 103:5 (2018), 836–840  mathnet  crossref  crossref  isi  elib
    48. V. A. Gritsenko, “Reflective modular forms and applications”, Russian Math. Surveys, 73:5 (2018), 797–864  mathnet  crossref  crossref  adsnasa  isi  elib
    49. N. V. Bogachev, “Classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4”, Izv. Math., 83:1 (2019), 1–19  mathnet  crossref  crossref  adsnasa  isi  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:1396
    Full text:634
    References:53
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020