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
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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},
publisher = {mathdoc},
volume = {58},
number = {2},
year = {1987},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1987_58_2_a8/}
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AU - Pham Huu Tiep
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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/