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Mat. Sb. (N.S.), 1967, Volume 72(114), Number 3, Pages 471–488 (Mi msb4099)  

This article is cited in 46 scientific papers (total in 48 papers)

Discrete groups generated by reflections in Lobachevskii spaces

È. B. Vinberg

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English version:
Mathematics of the USSR-Sbornik, 1967, 1:3, 429–444

Bibliographic databases:

UDC: 519.45
MSC: 22E40, 52Bxx, 20F55, 22E46, 22E10
Received: 21.10.1966

Citation: È. B. Vinberg, “Discrete groups generated by reflections in Lobachevskii spaces”, Mat. Sb. (N.S.), 72(114):3 (1967), 471–488; Math. USSR-Sb., 1:3 (1967), 429–444

Citation in format AMSBIB
\by \`E.~B.~Vinberg
\paper Discrete groups generated by reflections in Lobachevskii spaces
\jour Mat. Sb. (N.S.)
\yr 1967
\vol 72(114)
\issue 3
\pages 471--488
\jour Math. USSR-Sb.
\yr 1967
\vol 1
\issue 3
\pages 429--444

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    This publication is cited in the following articles:
    1. È. B. Vinberg, “Some examples of crystallographic groups in Lobachevskii spaces”, Math. USSR-Sb., 7:4 (1969), 617–622  mathnet  crossref  mathscinet  zmath
    2. E. M. Andreev, “On convex polyhedra in Lobachevskii spaces”, Math. USSR-Sb., 10:3 (1970), 413–440  mathnet  crossref  mathscinet  zmath
    3. O. V. Schwarzman, “Linear representations of groups generated by reflections”, Math. USSR-Sb., 11:3 (1970), 459–463  mathnet  crossref  mathscinet  zmath
    4. E. B. Vinberg, “Geometricheskie predstavleniya grupp Koksetera”, UMN, 25:2(152) (1970), 267–268  mathnet  mathscinet  zmath
    5. È. B. Vinberg, “Rings of definition of dense subgroups of semisimple linear groups”, Math. USSR-Izv., 5:1 (1971), 45–55  mathnet  crossref  mathscinet  zmath
    6. È. B. Vinberg, “Discrete linear groups generated by reflections”, Math. USSR-Izv., 5:5 (1971), 1083–1119  mathnet  crossref  mathscinet  zmath
    7. È. B. Vinberg, “On groups of unit elements of certain quadratic forms”, Math. USSR-Sb., 16:1 (1972), 17–35  mathnet  crossref  mathscinet  zmath
    8. G. A. Margulis, “Arithmetic properties of discrete subgroups”, Russian Math. Surveys, 29:1 (1974), 107–156  mathnet  crossref  mathscinet  zmath
    9. B. N. Kimel'fel'd, “Quasihomogeneous domains on a conformal sphere”, Russian Math. Surveys, 33:2 (1978), 233–234  mathnet  crossref  mathscinet  zmath
    10. V. V. Nikulin, “On arithmetic groups generated by reflections in Lobachevskii spaces”, Math. USSR-Izv., 16:3 (1981), 573–601  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123  mathnet  crossref  mathscinet  zmath  isi
    12. È. B. Vinberg, “Absence of crystallographic groups of reflections in Lobachevskii spaces of large dimension”, Funct. Anal. Appl., 15:2 (1981), 128–130  mathnet  crossref  mathscinet  zmath  isi
    13. J. Elstrodt, F. J. Grunewald, J. Mennicke, “Discontinuous groups on three-dimensional hyperbolic space: analytical theory and arithmetic applications”, Russian Math. Surveys, 38:1 (1983), 137–168  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. J.H Conway, “The automorphism group of the 26-dimensional even unimodular Lorentzian lattice”, Journal of Algebra, 80:1 (1983), 159  crossref  mathscinet  zmath
    15. È. B. Vinberg, “Hyperbolic reflection groups”, Russian Math. Surveys, 40:1 (1985), 31–75  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. 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
    17. Andreas W.M Dress, “Presentations of discrete groups, acting on simply connected manifolds, in terms of parametrized systems of Coxeter matrices—A systematic approach”, Advances in Mathematics, 63:2 (1987), 196  crossref  mathscinet  zmath
    18. C. Maclachlan, A. W. Reid, “The arithmetic structure of tetrahedral groups of hyperbolic isometries”, Mathematika, 36:2 (1989), 221  crossref  mathscinet  zmath  isi
    19. Maurice Kléman, “Curved crystals, defects and disorder”, Advances in Physics, 38:6 (1989), 605  crossref  mathscinet
    20. Mikhail Gromov, Richard Schoen, “Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 76:1 (1992), 165  crossref  mathscinet  zmath
    21. M. Karowski, R. Schrader, “A combinatorial approach to topological quantum field theories and invariants of graphs”, Comm Math Phys, 151:2 (1993), 355  crossref  mathscinet  zmath  adsnasa
    22. Marston D. E. Conder, Gaven J. Martin, “Cusps, triangle groups and hyperbolic 3-folds”, J Austral Math Soc, 55:2 (1993), 149  crossref  mathscinet  zmath
    23. F. W. Gehring, G. J. Martin, “Commutators, collars and the geometry of Möbius groups”, J Anal Math, 63:1 (1994), 175  crossref  mathscinet  zmath
    24. 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
    25. 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
    26. 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
    27. N.W. Johnson, R. Kellerhals, J.G. Ratcliffe, S.T. Tschantz, “Commensurability classes of hyperbolic Coxeter groups”, Linear Algebra and its Applications, 345:1-3 (2002), 119  crossref  mathscinet  zmath
    28. 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
    29. V. O. Bugaenko, “Klassifikatsiya mnogogrannikov Kokstera”, Matem. prosv., ser. 3, 7, MTsNMO, M., 2003, 82–106  mathnet
    30. 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
    31. 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
    32. V. V. Nikulin, “On Ground Fields of Arithmetic Hyperbolic Reflection Groups. II”, Mosc. Math. J., 8:4 (2008), 789–812  mathnet  crossref  mathscinet  zmath
    33. Agol, I, “Finiteness of arithmetic hyperbolic reflection groups”, Groups Geometry and Dynamics, 2:4 (2008), 481  crossref  mathscinet  zmath  isi
    34. Anna Felikson, Pavel Tumarkin, “On hyperbolic Coxeter polytopes with mutually intersecting facets”, Journal of Combinatorial Theory, Series A, 115:1 (2008), 121  crossref  mathscinet  zmath
    35. Benson Farb, “Group actions and Helly's theorem”, Advances in Mathematics, 222:5 (2009), 1574  crossref  mathscinet  zmath
    36. Inkang Kim, Bruno Klingler, P. Pansu, “Local quaternionic rigidity for complex hyperbolic lattices”, JMJ, 2010, 1  crossref  mathscinet
    37. B. Klingler, “Local rigidity for complex hyperbolic lattices and Hodge theory”, Invent math, 2010  crossref  mathscinet
    38. 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
    39. Vincent Emery, Ruth Kellerhals, “The three smallest compact arithmetic hyperbolic 5–orbifolds”, Algebr. Geom. Topol, 13:2 (2013), 817  crossref  mathscinet  zmath
    40. Kanghyun Choi, Suhyoung Choi, “The definability criteria for convex projective polyhedral reflection groups”, Geom Dedicata, 2014  crossref  mathscinet
    41. Martin Deraux, J.R.. Parker, Julien Paupert, “New non-arithmetic complex hyperbolic lattices”, Invent. math, 2015  crossref  mathscinet
    42. È. B. Vinberg, O. V. Schwarzman, “A Criterion of Smoothness at Infinity for an Arithmetic Quotient of the Future Tube”, Funct. Anal. Appl., 51:1 (2017), 32–47  mathnet  crossref  crossref  mathscinet  isi  elib
    43. 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
    44. 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
    45. N. V. Bogachev, “Classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4”, Izv. Math., 83:1 (2019), 1–19  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    46. N. Yu. Erokhovets, “Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions”, Proc. Steklov Inst. Math., 305 (2019), 78–134  mathnet  crossref  crossref  mathscinet  isi  elib
    47. Ratcliffe J., “Foundations of Hyperbolic Manifolds, 3Rd Edition”, Foundations of Hyperbolic Manifolds, 3Rd Edition, Graduate Texts in Mathematics, 149, Springer-Verlag Berlin, 2019, 1–800  crossref  isi
    48. Minos Axenides, Emmanuel Floratos, Stam Nicolis, “The Arithmetic Geometry of AdS$_2$ and its Continuum Limit”, SIGMA, 17 (2021), 004, 22 pp.  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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