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Mathematics of the USSR-Izvestiya, 1971, Volume 5, Issue 5, Pages 1083–1119
DOI: https://doi.org/10.1070/IM1971v005n05ABEH001203
(Mi im2148)
 

This article is cited in 69 scientific papers (total in 70 papers)

Discrete linear groups generated by reflections

È. B. Vinberg
References:
Abstract: We investigate linear groups generated by reflections in the faces of a convex polyhedral cone and operating discretely on an open convex cone. These groups generalize the discrete groups of motions in simply connected spaces of constant curvature, generated by reflection. Like the latter, they turn out to be Coxeter groups.
Received: 16.06.1970
Bibliographic databases:
UDC: 519.45
MSC: Primary 20H15, 50C15; Secondary 52F05, 52A25, 50C20
Language: English
Original paper language: Russian
Citation: È. B. Vinberg, “Discrete linear groups generated by reflections”, Math. USSR-Izv., 5:5 (1971), 1083–1119
Citation in format AMSBIB
\Bibitem{Vin71}
\by \`E.~B.~Vinberg
\paper Discrete linear groups generated by reflections
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 5
\pages 1083--1119
\mathnet{http://mi.mathnet.ru/eng/im2148}
\crossref{https://doi.org/10.1070/IM1971v005n05ABEH001203}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=302779}
\zmath{https://zbmath.org/?q=an:0247.20054}
Linking options:
  • https://www.mathnet.ru/eng/im2148
  • https://doi.org/10.1070/IM1971v005n05ABEH001203
  • https://www.mathnet.ru/eng/im/v35/i5/p1072
  • This publication is cited in the following 70 articles:
    1. Hongsheng Hu, “Reflection Representations of Coxeter Groups and Homology of Coxeter Graphs”, Algebr Represent Theor, 27:1 (2024), 961  crossref
    2. Jan Czajkowski, “Non-uniqueness Phase of Percolation on Reflection Groups in H3”, J Theor Probab, 2024  crossref
    3. Pyry Kuusela, Joseph McGovern, “Reflections in the mirror: Studying infinite Coxeter symmetries of GV-invariants”, Int. J. Mod. Phys. A, 2024  crossref
    4. Andre Lukas, Fabian Ruehle, “Symmetries of Calabi-Yau prepotentials with isomorphic flops”, J. High Energ. Phys., 2023:2 (2023)  crossref
    5. Annette Pilkington, “On reflection representations of Coxeter groups over non-commutative rings”, Communications in Algebra, 51:11 (2023), 4567  crossref
    6. Sami Douba, “Thin right‐angled Coxeter groups in some uniform arithmetic lattices”, Bulletin of London Math Soc, 54:5 (2022), 1653  crossref
    7. Károly Böröczky, Pavlos Kalantzopoulos, “Log-Brunn-Minkowski inequality under symmetry”, Trans. Amer. Math. Soc., 375:8 (2022), 5987  crossref
    8. Giovanni Paolini, Mario Salvetti, “Proof of the K(π,1) conjecture for affine Artin groups”, Invent. math., 224:2 (2021), 487  crossref
    9. Jeffrey Danciger, François Guéritaud, Fanny Kassel, “Proper affine actions for right-angled Coxeter groups”, Duke Math. J., 169:12 (2020)  crossref
    10. Daniel Allcock, Igor Dolgachev, “The tetrahedron and automorphisms of Enriques and Coble surfaces of Hessian type”, Annales Henri Lebesgue, 3 (2020), 1133  crossref
    11. Christophe Hohlweg, Jean-Philippe Préaux, Vivien Ripoll, “On the limit set of root systems of Coxeter groups acting on Lorentzian spaces”, Communications in Algebra, 48:3 (2020), 1281  crossref
    12. Michael Barot, Jesús Arturo Jiménez González, José-Antonio de la Peña, Algebra and Applications, 25, Quadratic Forms, 2019, 75  crossref
    13. Dimitry Leites, Oleksandr Lozhechnyk, “Inverses of Cartan matrices of Lie algebras and Lie superalgebras”, Linear Algebra and its Applications, 583 (2019), 195  crossref
    14. Anton A. Ayzenberg, “Torus actions of complexity 1 and their local properties”, Proc. Steklov Inst. Math., 302 (2018), 16–32  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Jeffrey Danciger, François Guéritaud, Fanny Kassel, “Convex cocompactness in pseudo-Riemannian hyperbolic spaces”, Geom Dedicata, 192:1 (2018), 87  crossref
    16. Hiroyasu TSUCHIHASHI, “Examples of four dimensional cusp singularities”, J. Math. Soc. Japan, 70:3 (2018)  crossref
    17. Anna Felikson, Pavel Tumarkin, “Acyclic cluster algebras, reflection groups, and curves on a punctured disc”, Advances in Mathematics, 340 (2018), 855  crossref
    18. C. Mokler, “Invariant convex subcones of the Tits cone of a linear Coxeter group”, Journal of Pure and Applied Algebra, 222:6 (2018), 1405  crossref
    19. E. B. Vinberg, M. A. Jibladze, A. G. Elashvili, “Moduli algebras of some non-semiquasihomogeneous singularities”, Funct. Anal. Appl., 51:2 (2017), 86–97  mathnet  crossref  crossref  isi  elib
    20. Ishida M., “Cusp Singularities and Quasi-Polyhedral Sets”, Algebraic Varieties and Automorphism Groups, Advanced Studies in Pure Mathematics, 75, ed. Masuda K. Kishimoto T. Kojima H. Miyanishi M. Zaidenberg M., Math Soc Japan, 2017, 163–182  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    References:98
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