The Niemeier lattices are defined to be the 24 even, self-dual lattices in 24 dimensions. Can anyone provide me with explicit bases for them, such that all the entries of the bases are rational numbers? Some basis are already given in the catalogue of lattices, but they either contain irrational entries or use matrices of dimensionality higher than 24, implementing the lattice as an appropriate subspace in a higher dimensional space, which is not what is wanted here. Is it possible to write down $24\times24$ matrices with rational entries that can be used as bases for the Niemeier lattices?
2026-03-25 06:32:02.1774420322
A basis with rational entries for the Niemeier lattices
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