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Classification of positive definite lattices

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arxiv math/9912236 v1 pith:AY2LOZQC submitted 1999-12-30 math.NT math.GR

classification math.NTmath.GR
keywords definitelatticespositivedimensionalsomealgorithmclassificationlattice
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In this paper we describe an algorithm for classifying orbits of vectors in Lorentzian lattices. The main point of this is that isomorphism classes of positive definite lattices in some genus often correspond to orbits of vectors in some Lorentzian lattice, so we can classify some positive definite lattices. As an application we give the classification of the 665 25-dimensional unimodular positive definite lattices and the 121 even 25 dimensional positive definite lattices of determinant 2. We also use this algorithm to show that there is a unique 26 dimensional unimodular positive definite lattice with no roots.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Supersymmetry and the Suzuki chain

    math.QA 2019-08 accept novelty 8.0 of 10

    All such SVOAs are exactly two infinite families plus nine exceptional examples, with automorphism groups ranging from symmetric groups to the Suzuki chain and related centralizers.

  2. A finite 6d supergravity landscape from anomalies

    hep-th 2025-07 conditional novelty 7.0 of 10

    Local and Dai-Freed global anomaly cancellation implies T ≤ 3003 and a finite 6d non-abelian supergravity landscape, with the extremal model [E8 x F4 x (G2 x SU(2))^2]^273.

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