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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 2, Pages 73–106 (Mi izv72)  

This article is cited in 12 scientific papers (total in 12 papers)

Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac–Moody algebras

V. V. Nikulin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We develop a theory of Lorentzian Kac–Moody algebras based on the theory of reflection groups in Lobachevskii spaces and on recent results of R. Borcherds.

DOI: https://doi.org/10.4213/im72

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English version:
Izvestiya: Mathematics, 1996, 60:2, 305–334

Bibliographic databases:

UDC: 512.75+512.817+512.818
MSC: 14D20, 10D20, 17B65
Received: 25.04.1995

Citation: V. V. Nikulin, “Reflection groups in Lobachevskii spaces and the denominator identity for Lorentzian Kac–Moody algebras”, Izv. RAN. Ser. Mat., 60:2 (1996), 73–106; Izv. Math., 60:2 (1996), 305–334

Citation in format AMSBIB
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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. V. A. Gritsenko, V. V. Nikulin, “Igusa modular forms and 'the simplest' Lorentzian Kac–Moody algebras”, Sb. Math., 187:11 (1996), 1601–1641  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Gritsenko V.A., Nikulin V.V., “Automorphic forms and Lorentzian Kac-Moody algebras. Part I”, International Journal of Mathematics, 9:2 (1998), 153–199  crossref  mathscinet  zmath  isi  elib
    3. Gritsenko V.A., Nikulin V.V., “Automorphic forms and Lorentzian Kac-Moody algebras. Part II”, International Journal of Mathematics, 9:2 (1998), 201–275  crossref  mathscinet  zmath  isi  elib
    4. 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
    5. Gritsenko V.A., Nikulin V.V., “The arithmetic mirror symmetry and Calabi-Yau manifolds”, Communications in Mathematical Physics, 210:1 (2000), 1–11  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. 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
    7. Ji L., “Buildings and their application in geometry and topology”, Asian Journal of Mathematics, 10:1 (2006), 11–80  crossref  mathscinet  zmath  isi  scopus  scopus
    8. V.V.. Nikulin, “Elliptic Fibrations On K3 Surfaces”, Proceedings of the Edinburgh Mathematical Society, 2013, 1  crossref  mathscinet  scopus  scopus
    9. Belolipetsky M., Mcleod J., “Reflective and Quasi-Reflective Bianchi Groups”, Transform. Groups, 18:4 (2013), 971–994  crossref  mathscinet  zmath  isi  scopus
    10. Allcock D., “Root Systems For Lorentzian Kac-Moody Algebras in Rank 3”, Bull. London Math. Soc., 47:2 (2015), 325–342  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    11. Belolipetsky M., “Arithmetic hyperbolic reflection groups”, Bull. Amer. Math. Soc., 53:3 (2016), 437–475  crossref  mathscinet  zmath  isi  elib  scopus
    12. 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  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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