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Tr. Mosk. Mat. Obs., 1984, Volume 47, Pages 68–102 (Mi mmo444)  

This article is cited in 25 scientific papers (total in 27 papers)

Absence of crystallographic groups of reflections in Lobachevski˜{i} spaces of large dimension

È. B. Vinberg

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UDC: 519.46
MSC: Primary 22E40; Secondary 20H15, 51E15
Received: 10.12.1980

Citation: È. B. Vinberg, “Absence of crystallographic groups of reflections in Lobachevski˜{i} spaces of large dimension”, Tr. Mosk. Mat. Obs., 47, MSU, M., 1984, 68–102

Citation in format AMSBIB
\by \`E.~B.~Vinberg
\paper Absence of crystallographic groups of reflections in Lobachevski\~{i} spaces of large dimension
\serial Tr. Mosk. Mat. Obs.
\yr 1984
\vol 47
\pages 68--102
\publ MSU
\publaddr M.

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    This publication is cited in the following articles:
    1. È. B. Vinberg, “Hyperbolic reflection groups”, Russian Math. Surveys, 40:1 (1985), 31–75  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. N. Prokhorov, “The absence of discrete reflection groups with noncompact fundamental polyhedron of finite volume in Lobachevskii space of large dimension”, Math. USSR-Izv., 28:2 (1987), 401–411  mathnet  crossref  mathscinet  zmath
    3. A. G. Khovanskii, “Hyperplane sections of polyhedra, toroidal manifolds, and discrete groups in Lobachevskii space”, Funct. Anal. Appl., 20:1 (1986), 41–50  mathnet  crossref  mathscinet  zmath  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. III”, Math. USSR-Izv., 35:3 (1990), 657–675  mathnet  crossref  mathscinet  zmath
    6. V. V. Nikulin, “Del Pezzo surfaces with log-terminal singularities”, Math. USSR-Sb., 66:1 (1990), 231–248  mathnet  crossref  mathscinet  zmath  isi
    7. V. V. Nikulin, “Algebraic three-folds and the diagram method”, Math. USSR-Izv., 37:1 (1991), 157–189  mathnet  crossref  mathscinet  zmath  adsnasa
    8. G. G. Ilyuta, “Characterization of real Coxeter–Dynkin diagrams of simple singularities”, Russian Math. Surveys, 50:3 (1995), 620–622  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. 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
    10. 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
    11. 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
    12. 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
    13. V. O. Bugaenko, “Klassifikatsiya mnogogrannikov Kokstera”, Matem. prosv., ser. 3, 7, MTsNMO, M., 2003, 82–106  mathnet
    14. 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
    15. 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
    16. R. M. Garipov, “Crystallographic classes in the Minkowski space $R_{1,2}$. I. Theorems”, J. Appl. Industr. Math., 2:4 (2008), 484–500  mathnet  crossref  mathscinet  elib
    17. V. V. Nikulin, “Finiteness of the number of arithmetic groups generated by reflections in Lobachevsky spaces”, Izv. Math., 71:1 (2007), 53–56  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. V. V. Nikulin, “On Ground Fields of Arithmetic Hyperbolic Reflection Groups. II”, Mosc. Math. J., 8:4 (2008), 789–812  mathnet  crossref  mathscinet  zmath
    19. 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
    20. 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
    21. Viacheslav V. Nikulin, “Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups”, Proc. Steklov Inst. Math., 273 (2011), 229–237  mathnet  crossref  mathscinet  zmath  isi  elib
    22. V. M. Buchstaber, N. Yu. Erokhovets, M. Masuda, T. E. Panov, S. Park, “Cohomological rigidity of manifolds defined by 3-dimensional polytopes”, Russian Math. Surveys, 72:2 (2017), 199–256  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    23. 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
    24. N. V. Bogachev, A. Yu. Perepechko, “Vinberg's Algorithm for Hyperbolic Lattices”, Math. Notes, 103:5 (2018), 836–840  mathnet  crossref  crossref  isi  elib
    25. 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  mathscinet  zmath  isi  scopus
    26. 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
    27. E. S. Stuken, “Svobodnye algebry avtomorfnykh form Gilberta”, Funkts. analiz i ego pril., 53:1 (2019), 49–66  mathnet  crossref  elib
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