On even unimodular positive definite quadratic lattices of rank 32

Abstract

Let Z be the ring of rational integers, and ~ the field of rational numbers. A finitely generated Z-module L in Q" with a positive definite metric is called a quadratic lattice. Since we treat only the quadratic lattices, we shall omit the adjectives "positive definite quadratic". A lattice L is integral if L satisfies (x ,y)sZ for any x, y e L where ( , ) is the bilinear form associated to the metric. The dual L e of L is defined by