Configurations of Extremal Even Unimodular Lattices

TL;DR

This paper extends previous results on extremal even unimodular lattices, demonstrating that for ranks 56, 72, and 96, these lattices are generated by their minimal-norm vectors, deepening understanding of their structure.

Contribution

The paper proves that extremal even unimodular lattices of ranks 56, 72, and 96 are generated by their minimal vectors, extending earlier results to these specific ranks.

Findings

Lattices of rank 56, 72, and 96 are generated by minimal vectors.

Extension of Ozeki's results to new lattice ranks.

Structural insight into extremal even unimodular lattices.

Abstract

We extend the results of Ozeki on the configurations of extremal even unimodular lattices. Specifically, we show that if L is such a lattice of rank 56, 72, or 96, then L is generated by its minimal-norm vectors.