Invariant Lattices, the Leech Lattice and its Even Unimodular Analogues in the Lie Algebras A_{p-1}
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.
- Publication:
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Sbornik: Mathematics
- Pub Date:
- February 1987
- DOI:
- 10.1070/SM1987v058n02ABEH003113
- Bibcode:
- 1987SbMat..58..435B