General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

Mat. Sb. (N.S.), 1986, Volume 130(172), Number 4(8), Pages 435–464 (Mi msb1885)  

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

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.

Full text: PDF file (1498 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1987, 58:2, 435–465

Bibliographic databases:

Document Type: Article
UDC: 512.54+512.81
MSC: Primary 11H06, 17B05; Secondary 20B25
Received: 23.01.1986

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
\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
\jour Math. USSR-Sb.
\yr 1987
\vol 58
\issue 2
\pages 435--465

Linking options:

    SHARE: FaceBook Twitter Livejournal

    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. K. S. Abdukhalikov, “On invariant lattices in Lie algebras of type $A_{q-1}$”, Russian Math. Surveys, 43:1 (1988), 227–228  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Pham Huu Tiep, “Irreducible orthogonal decompositions in Lie algebras”, Math. USSR-Sb., 68:1 (1991), 257–275  mathnet  crossref  mathscinet  zmath  isi
    3. Pham Huu Tiep, “Lattices of non-radical type in the Lie algebras $B_3$ and $D_4$”, Russian Math. Surveys, 44:1 (1989), 247–248  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Kostrikin A., Tiep PH., “Irreducible Orthogonal Decompositions of Simple Lie-Algebra of Type an”, 314, no. 4, 1990, 782–786  mathscinet  zmath  isi
    5. Pham Huu Tiep, “Weil representations of finite symplectic groups, and Gow lattices”, Math. USSR-Sb., 73:2 (1992), 535–555  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. V. P. Burichenko, “On a special loop, the discon form, and the lattice connected with $O_7(3)$”, Math. USSR-Sb., 74:1 (1993), 145–167  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Pham Huu Tiep, “A classification of the irreducible orthogonal decompositions of the simple complex Lie algebras of type Bn”, Communications in Algebra, 19:10 (1991), 2729  crossref
    8. Tiep PH., “Reduction Theorem for Invariant Lattices of the Type-an”, 319, no. 1, 1991, 78–82  mathscinet  zmath  isi
    9. K. S. Abdukhalikov, “Integral invariant lattices in Lie algebras of type $A_{p^m-1}$”, Russian Acad. Sci. Sb. Math., 78:2 (1994), 447–478  mathnet  crossref  mathscinet  zmath  isi
    10. V. P. Burichenko, “Invariant lattices in the Steinberg module and their isometry groups”, Russian Acad. Sci. Sb. Math., 80:2 (1995), 519–529  mathnet  crossref  mathscinet  zmath  isi
    11. Vladimir P. Burichenko, Pham Huu Tiep, “Invariant lattices of typeF4andF4: the automorphism groups”, Communications in Algebra, 21:12 (1993), 4641  crossref
    12. K. S. Abdukhalikov, “Integral lattices associated with a finite affine group”, Russian Acad. Sci. Sb. Math., 83:2 (1995), 431–443  mathnet  crossref  mathscinet  zmath  isi
    13. K. S. Abdukhalikov, “Modular permutation representations of $\operatorname {PSL}(n,p)$”, Sb. Math., 188:8 (1997), 1107–1117  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. K. S. Abdukhalikov, “Automorphism groups of invariant lattices in the Steinberg module of groups of Lie type of odd characteristic”, Sb. Math., 189:9 (1998), 1273–1294  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:414
    Full text:107
    First page:1

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019