On classifying Minkowskian sublattices

Details On classifying Minkowskian sublattices On classifying Minkowskian sublattices

2009-04-20

arxiv.org/abs/0904.3110v3

Mathematics

Number Theory

34 pages; incorporated referee comments

Scientific paper

10.1090/S0025-5718-2011-02528-7

Let $\Lambda$ be a lattice in an $n$-dimensional Euclidean space $E$ and let $\Lambda'$ be a Minkowskian sublattice of $\Lambda$, that is, a sublattice having a basis made of representatives for the Minkowski successive minima of $\Lambda$. We extend the classification of possible $\Z/d\Z$-codes of the quotients $\Lambda/\Lambda'$ to dimension~$9$, where $d\Z$ is the annihilator of $\Lambda/\Lambda'$.

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