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Mathematics of the USSR-Sbornik, 1987, Volume 58, Issue 2, Pages 435–465
DOI: https://doi.org/10.1070/SM1987v058n02ABEH003113 (Mi sm1885) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Invariant lattices, the Leech lattice and its even unimodular analogues in the Lie algebras $A_{p-1}$

A. I. Bondal, A. I. Kostrikin, Pham Huu Tiep
English version PDF (1516 kB) Citations (14)
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DOI: https://doi.org/10.1070/SM1987v058n02ABEH003113
Abstract: For any prime $p>2$ a classification (up to similarity) is given of all invariant integral lattices that correspond to an orthogonal decomposition of the Lie algebra $A_{p-1}$. Even unimodular lattices without roots are distinguished. For $p=5$ they contain the Leech lattice. For some of the resulting lattices the automorphism groups are studied, and lower bounds for the minimal length of vectors are obtained.
Figures: 2.
Bibliography: 17 titles.
Received: 23.01.1986
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1986, Volume 130(172), Number 4(8), Pages 435–464
Bibliographic databases:
Document Type: Article
UDC: 512.54+512.81
MSC: Primary 11H06, 17B05; Secondary 20B25
Language: English
Original paper language: Russian
Citation: A. I. Bondal, A. I. Kostrikin, Pham Huu Tiep, “Invariant lattices, the Leech lattice and its even unimodular analogues in the Lie algebras $A_{p-1}$”, Mat. Sb. (N.S.), 130(172):4(8) (1986), 435–464; Math. USSR-Sb., 58:2 (1987), 435–465
Citation in format AMSBIB
\Bibitem{BonKosPha86}
\by A.~I.~Bondal, A.~I.~Kostrikin, Pham Huu Tiep
\paper Invariant lattices, the Leech lattice and its even unimodular analogues in the Lie~algebras~$A_{p-1}$
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 130(172)
\issue 4(8)
\pages 435--464
\mathnet{http://mi.mathnet.ru/sm1885}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=867336}
\zmath{https://zbmath.org/?q=an:0634.10028}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 2
\pages 435--465
\crossref{https://doi.org/10.1070/SM1987v058n02ABEH003113}
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  • https://doi.org/10.1070/SM1987v058n02ABEH003113
  • https://www.mathnet.ru/eng/sm/v172/i4/p435
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:689
    Russian version PDF:228
    English version PDF:27
    References:66
    First page:1
     
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