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Zbl 1075.11048
Kitazume, Masaaki; Munemasa, Akihiro
Even unimodular Gaussian lattices of rank 12. (English)
[J] J. Number Theory 95, No. 1, 77-94 (2002). ISSN 0022-314X; ISSN 1096-1658/e

Summary: We classify even unimodular Gaussian lattices of rank 12, that is, even unimodular integral lattices of rank 12 over the ring of Gaussian integers. This is equivalent to the classification of the automorphisms $\tau $ with $\tau ^2 = -1 $ in the automorphism groups of all the Niemeier lattices, which are even unimodular (real) integral lattices of rank 24. There are 28 even unimodular Gaussian lattices of rank 12 up to equivalence.

MSC 2000:: *11H06 Lattices and convex bodies (number theoretic results)
11H56 Automorphism groups of lattices

Keywords: Niemeier lattice; Hermitian form; root system; automorphism group; Weyl group

Cited in: Zbl 1229.11062

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