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arXiv · 1705.06525

Quaternary quadratic lattices over number fields

Markus Kirschmer·Gabriele Nebe
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Abstract

We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q).

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Markus Kirschmer, Gabriele Nebe. 2018-09-10. Quaternary quadratic lattices over number fields. https://doi.org/10.1142/s1793042119500131

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