Quaternary quadratic lattices over number fields

被引：1

作者：

Kirschmer, Markus ^{[1
]}

Nebe, Gabriele ^{[1
]}

机构：

[1] Rhein Westfal TH Aachen, Lehrstuhl Math D, D-52056 Aachen, Germany

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2019年 / 15卷 / 02期

关键词：

Quaternary quadratic forms; lattices over totally real fields; genera of lattices; orders in quaternion algebras; class numbers; classification algorithm; CLASSIFICATION; FORMS;

D O I：

10.1142/S1793042119500131

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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).

引用

页码：309 / 325

页数：17

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