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Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order. (English) Zbl 0886.11021

The authors apply their generalization of Kneser’s neighboring method to determine the genus of hermitian unimodular lattices of rank 8 over the Hurwitz order \({\mathfrak M}\), as well as the genus of \({\mathfrak M}\)-lattices corresponding to unimodular \(\mathbb Z\)-lattices. Several tables containing information on the associated bipartite graph (see definition 2.5 of the paper) are included, and explicit constructions are given.
Reviewer: K.Roegner (Berlin)

MSC:

11E12 Quadratic forms over global rings and fields
11H55 Quadratic forms (reduction theory, extreme forms, etc.)
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