Geodesic
Invariant lattices, the Leech lattice and its even unimodular analogues in the Lie algebras $A_{p-1}$
Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 435-465 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{SM_1987_58_2_a8,
     author = {A. I. Bondal and A. I. Kostrikin and Pham Huu Tiep},
     title = {Invariant lattices, the {Leech} lattice and its even unimodular analogues in the {Lie~algebras~}$A_{p-1}$},
     journal = {Sbornik. Mathematics},
     pages = {435--465},
     year = {1987},
     volume = {58},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_58_2_a8/}
}
TY  - JOUR
AU  - A. I. Bondal
AU  - A. I. Kostrikin
AU  - Pham Huu Tiep
TI  - Invariant lattices, the Leech lattice and its even unimodular analogues in the Lie algebras $A_{p-1}$
JO  - Sbornik. Mathematics
PY  - 1987
SP  - 435
EP  - 465
VL  - 58
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1987_58_2_a8/
LA  - en
ID  - SM_1987_58_2_a8
ER  - 
%0 Journal Article
%A A. I. Bondal
%A A. I. Kostrikin
%A Pham Huu Tiep
%T Invariant lattices, the Leech lattice and its even unimodular analogues in the Lie algebras $A_{p-1}$
%J Sbornik. Mathematics
%D 1987
%P 435-465
%V 58
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1987_58_2_a8/
%G en
%F SM_1987_58_2_a8
A. I. Bondal; A. I. Kostrikin; Pham Huu Tiep. Invariant lattices, the Leech lattice and its even unimodular analogues in the Lie algebras $A_{p-1}$. Sbornik. Mathematics, Tome 58 (1987) no. 2, pp. 435-465. http://geodesic.mathdoc.fr/item/SM_1987_58_2_a8/

[1] Bondal A. I., “Invariantnye reshetki tipa $A_{p-1}$”, Vestn. MGU. Ser. 1. Matem., mekh., 1986, no. 1, 52–54 | MR | Zbl

[2] Burbaki N., Gruppy i algebry Li, gl. IV–VI, Mir, M., 1972 | MR | Zbl

[3] Veil A., Osnovy teorii chisel, Mir, M., 1972 | MR

[4] Venkov B. B., “O klassifikatsii tselochislennykh chetnykh 24-mernykh kvadratichnykh form”, Tr. MIAN, 148 (1978), 65–76 | MR | Zbl

[5] Venkov B. B., Unimodulyarnye evklidovy reshetki, Dis. d-ra fiz.-matem. nauk, LGU, L., 1984, s. 1–159

[6] Erokhin V. A., “O gruppakh avtomorfizmov 24-mernykh chetnykh unimodulyarnykh reshetok”, Zap. nauchn. seminarov LOMI, 116 (1982), 68–73 | MR | Zbl

[7] Kassels Dzh., Ratsionalnye kvadratichnye formy, Mir, M., 1982 | MR

[8] Kostrikin A. I., Kostrikin I. A., Ufnarovskii V. A., “Ortogonalnye razlozheniya prostykh algebr Li (tip $A_n$)”, Tr. MIAN, 158 (1981), 105–120 | MR | Zbl

[9] Kostrikin A. I., Kostrikin I. A., Ufnarovskii V. A., “Invariantnye reshetki tipa $G_2$ i ikh gruppy avtomorfizmov”, Tr. MIAN, 165 (1984), 79–97 | MR | Zbl

[10] Serr Zh.-P., Kurs arifmetiki, Mir, M., 1972 | MR | Zbl

[11] Fam Khyu Tep, “Ob odnoi konstruktsii chetnykh unimodulyarnykh reshetok”, Vestn. MGU. Ser. 1. Matem., mekh., 1986, no. 1, 54–56

[12] Conway J. H., “A group of order 8315553613086720000”, Bull. London Math. Soc., 1 (1969), 79–88 | DOI | MR | Zbl

[13] Conway J. H., “A Characterizaiion of the Leech's Lattice”, Invent. Math., 7 (1969), 137–142 | DOI | MR | Zbl

[14] Conway J. H., Sloane N. J. A., “Twenty-three constructions for the Leech lattice”, Proc. Roy. Soc. London, Ser. A, 381 (1982), 275–283 | DOI | MR | Zbl

[15] Frenkel I. B., Lepowsky J., Meurman A., “A natural representation of the Rischer–Griess Monster with the modular function $J$ as character”, Proc. Nat. Acad. Sci. U.S.A., 81 (1984), 3256–3260 | DOI | MR | Zbl

[16] Niemeier H. V., “Definite quadratische Formen der Dimension 24 und Discriminant I”, J. Number Theory, 5:2 (1973), 142–178 | DOI | MR | Zbl

[17] Smith P. E., Ph. D. diss., Cambridge (England), 1975