• Corpus ID: 237581599

Even Unimodular Lattices from Quaternion Algebras

  title={Even Unimodular Lattices from Quaternion Algebras},
  author={Laia Amor'os and Mohamed Taoufiq Damir and Camilla Hollanti},
We review a lattice construction arising from quaternion algebras over number fields and use it to obtain some known extremal and densest lattices in dimensions 8 and 16. The benefit of using quaternion algebras over number fields is that the dimensionality of the construction problem is reduced by 3/4. We explicitly construct the E8 lattice (resp. E 2 8 and Λ16) from infinitely many quaternion algebras over real quadratic (resp. quartic) number fields and we further present a density result on… 

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