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Even unimodular Gaussian lattices of rank 12. (English) Zbl 1075.11048
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:
 11H06 Lattices and convex bodies (number-theoretic aspects) 11H56 Automorphism groups of lattices
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##### References:
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