Quaternary quadratic lattices over number fields
Number Theory
2018-09-11 v2
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).
Cite
@article{arxiv.1705.06525,
title = {Quaternary quadratic lattices over number fields},
author = {Markus Kirschmer and Gabriele Nebe},
journal= {arXiv preprint arXiv:1705.06525},
year = {2018}
}