On lattices of maximal index two

Mathematics – Number Theory

Scientific paper

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25 pages

Scientific paper

The maximal index of a Euclidean lattice L of dimension n is the maximal
index of the sub-lattices of L spanned by n independent minimal vectors of L.
In this paper, we prove that a perfect lattice of maximal index two not
provided by a cross-section has dimension at most 5.

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