# Even Unimodular Lattices from Quaternion Algebras

@inproceedings{Amoros2021EvenUL, title={Even Unimodular Lattices from Quaternion Algebras}, author={Laia Amor'os and Mohamed Taoufiq Damir and Camilla Hollanti}, year={2021} }

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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