Binary Hermitian Lattices over Number Fields

Abstract

In a previous paper the authors developed an algorithm to classify certain quaternary quadratic lattices over totally real fields. The present article applies this algorithm to the classification of binary Hermitian lattices over totally imaginary fields. We use it in particular to classify the 48-dimensional extremal even unimodular lattices over the integers that admit a semilarge automorphism.

Keywords:

• binary Hermitian forms
• Hermitian lattices over CM-fields
• genera of lattices
• orders in quaternion algebras
• class numbers
• classification algorithm

2010 AMS Subject Classification:

• 11E20
• 11E41
• 11E12
• 11R52

Additional information

Funding

The research is supported by the DFG within the framework of the SFB TRR 195.