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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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